4. (a) What is an arithmetic sequence? Write a formula for the nth term of an arithmetic sequence. (b) Write a formula for the arithmetic sequence that starts as follows: 3, 8, ... Write the first five tems of this sequence. (c) Write two different formulas for the sum of the first n terms of an arithmetic sequence. (d) Find the sum of the first 20 terms of the sequence in part (b).

Q: What is a geometric sequence? Write an expression for the nth term of a geometric sequence that has…

A: Geometric Sequence: A sequence in which each term is found by multiplying the previous term by a…

Q: 1. The first term of an arithmetic sequence is 5. The eleventh term is 125. What is the common…

A: GivenFirst term of arithmetic sequence 'a' = 5Eleventh term of arithemetic sequece 'T_11' = 125

Q: Find the common difference and the sum of the first 5 terms of the arithmetic sequence. an = 5n – 2

A:

Q: What is the formula for the arithmetic sequence if the sum of the same sequence is given by sn 2n +…

A:

Q: 10. Find the tenth term of a geometric sequence with fifth and sixth terms 2, and 3, respectively.

A:

Q: Find the infinite sum of the geometric sequence with a = 6, r 2 if it exists.

A: Here,  a=6, r=2/6

Q: た 2 白 Find the sum of the indicated number of terms of the geometric sequence. -4, 12, -36, ...; n =…

A: Consider the given series.

Q: 41. Find the sum of the first 70 terms of the arithmetic sequence with first term 10 and common…

A: "The student ask for the question number 41, so I am solving the question number 41." Given that,…

Q: A. Write the first five terms of the sequence with the fırst term 2 and a common difference of 3. B.…

A: Given A). a1=2  and d=3 b). a1=3 and common ratio (r)=-4

Q: Write an expression that gives the requested term. The 13th term of the geometric sequence with…

A:

Q: bus travels 250m in the first minute, 500m in the second minute, 1000m in the third minute and so on…

A:

Q: Determine the sum of the first four terms of the geometric sequence where a = 3 and r = 2.

A:

Q: how do i find the first five terms of the arithmetic sequence using the recursive formula? step by…

A: Given nth term of the sequence is as below

Q: 2. The first term of an arithmetic sequence is -15 and the fifth term is 13. Find a40.

A: We can find the answer as below.

Q: Use the formula for the sum of the first n terms of a geometric sequence to:Find the sum of the…

A: Given: 3, -6, 12, -24, . . . . is the geometric sequence. To find: the sum of the first 11 terms of…

Q: An arithmetic sequence is a sequence in which each term after the first differs from the preceding…

A: Given That: Definition of Arithmetic sequence.

Q: Find the 2nd, 3rd, and 4th terms of the geometric sequence whose first term is 6 and common ratio is…

A: The nth term of a sequence can be obtained by the formula an=arn-1,where r is the common ratio and…

Q: An arithmetic sequence whose first term is 2 has the property that its second, third, and seventh…

A: Given The arithmetic sequence whose first term is 2 has the property that its second, third, and…

Q: 3. Evaluate to find the sum of the first 7 terms in the arithmetic sequence. 8, 2, -4, ...- 28

A:

Q: 2a. Find a formula for the nth term of the arithmetic sequence below. 1,_,4, , 7, ...

A: Solve by formula

Q: What is the 12th term in the geometric sequence -9,27,-81...? A) -531441 B) 1594323 C) -4782969 D)…

A: The geometric sequence is given by -9, 27,-81,········ To evaluate : The 12th term in the geometric…

Q: Find the explicit formula for the general nth term of the geometric sequence described below.…

A:

Q: 6.1 Find the hundredth term of the arithmetic sequence with the first term 2 And ninth term 18

A:

Q: What is the explicit formula for a geometric sequence?

A:

Q: 3. The 3rd term of a geometric sequence is 12 and the 7th term is 192. Determine the 13th term.

A:

Q: 2. (a) What is a recursively defined sequence? (b) Find the first four terms of the sequence…

A: (a) A recursive defined sequence is a sequence in which terms are defined using one or more previous…

Q: 4 Chose the formula for the nth term of the Geometric Sequence: 6, 4, 4, 10

A:

Q: Find a formula for the nth term of the geometric sequence. Then find the indicated nth term of the…

A: Given: The geometric sequence,  2, 22, 242, ... To find: The formula for the nth term of the…

Q: The middle term of an arithmetic sequence equals 17, the last term = 32, and the fourth term = 11.…

A: Given middle term = 17 Last term = 32 Fourth term = 11 T4 = a+3d = 11 Middle term = T6 = a+5d = 17…

Q: 6. Find the first 4 terms and the 12th term of the geometric sequence: a, =100,000 and r = -0.2 ɑ1 =…

A:

Q: Give an example of an arithmetic sequence and geometric sequence, each with at least 6 terms

A:

Q: Find the common difference and the sum of the first 8 terms of the arithmetic sequence. an = 4(n-1)…

A:

Q: 4 Find the sum of the first 3 terms of a geometric sequence with a = 18 and r= 3 The sum is

A:

Q: Find the 75th term of the arithmetic sequence with first term 2 and common difference -1/2.

A:

Q: Write down the first five terms of the geometric sequence which has first term 1 and common ratio ½.

A: First term = a = 1 Common ratio = r = 1/2

Q: An arithmetic sequence is a sequence in which the___between successive terms is constant.

A: An arithmetic sequence is a sequence in which  the difference between successive terms is…

Q: Example 6: Find the sum of the first 30 terms of the arithmetic sequence 3,7,11, 15, ..

A: Given- Consider the arithmetic sequence 3,7,11,15......  To Find- The sum of the first 30 terms.…

Q: Find the nth term of the arithmetic sequence {a,} whose initial term a and common difference d are…

A:

Q: 7. a. Find the general term for the geometric sequence -1, -2, -4, -8, . ... b. Find the 12th term…

A:

Q: 12. Given that the 5th and 11th terms of an Arithmetic Sequence are 26 and -16, respectively,…

A:

Q: 4. An arithmetic sequence has the first term of 10 and a common difference of-2. Find the sum of the…

A: Topic = Arithmetic sequence

Q: 3) Find the sum of the first 12 terms of the geometric sequence-3,-6,-12,-24,..

A: We can solve as follows

Q: 1. Find the first 11 terms of an arithmetic sequence in which the third term is 10 and the eleventh…

A:

Q: 15. Write the general formula in finding the sum of the terms of a FINITE geometric sequence.

A: We use concept of difference of sequence..

Q: Use the formula for the sum of the first n terms of a geometric sequence to:Find the sum of the…

A: Write the first term and the common ratio of the sequence. a=3,r=63=2

Q: A) Find the sum of the first fifteen term of arithmetic sequence with first term 20 and common…

A:

Q: Use the formula for the sum of the first n terms of a geometric sequence to find the sum of the…

A: Given that the geometric sequence is 7,14,28,56,112,....

Q: Determine the sum of the first five terms of the geometric sequence where a = 3 and r=2. ... The sum…

A: The formula to evaluate the sum of n terms of a geometric sequence is Sn=arn-1r-1, if r≠1, where a…

Q: 9. Find the value of x and y if x-y, 7x+y-1, and -5y are consecutive terms of an arithmetic…

A: As per the instruction, we will be answering only the first question. We need to find all the value…

Q: Write the first 5 terms of Geometric sequence whose nth term is an = 6(1/2)n-

A: We will solve the problem