Patterns are regular, recurring, and repeating forms or designs that are commonly observed in natural objects. * True False   3. Which of the numbers does not fit into the series 35, 118, 280, 600, 1238, 2504, 5036? *   a. 1238 b. 280 c. 118 d. 600

Q: What is the value of d in the arithmetic series 8 +b + c + d + e +... if the sum of the first 87…

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Q: 1. Find the sum to infinity of the GP: 7 + 2/7 + 4/343 + 8/16087+... . Find the least number of…

A: Since you have posted multiple questions and not specified which questions to be solved. So we will…

Q: Find the sum of the series. 97 8 n!

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Q: Find 41 term of series 12,18,24..

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Q: How many terms are there in each of the following sequences? a. 1, 3, 32, 33 3399 b. 11, 17, 23, 29,…

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Q: Consider the following series 14+98+686+4802+⋯ a) Does this series have an infinite sum? Why? b) If…

A: We will find out the required sum.

Q: Find the sum of the first nine terms of the geometric series 8, -24, 72... A.)-19,6893 B.)19,691…

A: We have to find the sum of nine terms of geometric series 8,-24,72..... We know that if…

Q: 7. Write the geometric series lin 3-notation and find its sum. 24 48 96

A: Given an infinite series. We will find sum for both finite and infinite case

Q: 4. There is a stack of logs in the backyard. 15 logs are in the first layer; 14, in the second; 13,…

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Q: How would you classify the sequence 28,21, 15, 10, 6, ... .? ...... A. Arithmetic Series B.…

A: Difference between terms is equal So this is arithmetic series.  Option A is correct

Q: What is the value of c in the arithmetic series 5 + b + c + d + e +.. if the sum of the first 80…

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Q: If a,,ª,,.....ª, is an AP of non-zero terms, what is the sum of the following series? 1 9,9₂ azaz

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Q: 13. What comes in place of the blank in the following series?WE, SG, PJ, LN,

A: Since you have asked multiple questions here, we will solve the first question for you . To get the…

Q: Show that 1 1 1 3 1.3 2.4 3.5 4 [Hint: Find an expression for a general term in the sum and see if…

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Q: Find the 30th term of the series 4,5,9,14, ...

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Q: d) How many different three letter sequences can be formed using the letters in the word OPTIC.…

A: Topic- permutations and combinations

Q: Which of the following statements is true about Fibonacci sequence and the Golden ratio? O a. The…

A: We know that, Golden ratio=limn→∞Fn+1Fn

Q: if the 8th term in an arithmatic series is 39 and the 20th term -33 what is the common difference

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Q: 12. What is the next term in the Fibonacci sequence 1, 1, 2, 3, 5, 8 ...? а. 11 b. 12 С. 13 d. 14

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Q: Find 21st term of series  12,16,18

A: n=21 tn=a+n-1d a=12, d=4 t21=12+204 t21=12+80

Q: Find the sum of the arithmetic series n = 10, an =41S n=230 show work

A: an =a+(n-1)d  and sn = n(a+l)/2 where l = an

Q: II. Answer the following: 1. Calculate for the perimeter and area of a regular 13-gon of side length…

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Q: 1111 -216 + 36 – 6+ 1., S.

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Q: If an 3 what is the true about the series a,? 2"

A: Let we have given a series ∑an, we need to determine whether the series is convergent or not.Now…

Q: . How would you classify the sequence 28, 21, 15, 10,6, B. Geometric Series A. Arithmetic Series D.…

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Q: Find out the number of terms (n) in the series below

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Q: Write the given series in 3-+- 3 +. 4 8

A: Given series forms infinite term of geometrical series

Q: Find the sum, if it existsof the Infinite geometric series S=21+9+3.86+

A: solution:- its geometric series because the common ration is same between the digits

Q: 1111 -216 + 36 - 6 + 1., S= 6.

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Q: What is the sum of the first 12 terms in the series shown beloW! 1.5 4.5 + 13.5 -40.5 +

A: Given sequence is: 1.5-4.5+13.5-40.5+...upto 12 termsTo find the sum of first 12 terms  The formula…

Q: Evaluate the telescoping series or state whether the series diverges. (If the quantity diverges,…

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Q: Find 81 term of series 41,43,45...

A: As we know that; The expression for the nth term of the arithmetic sequence is: Tn=a+n-1d Where, a…

Q: What is the sum of the first 80 terms of the series 10 +7+4+...

A: Given that: 10+7+4+...

Q: What is the sum of the first 14 terms of the series 9+2-5-12-19-...? O-25 O-98 O-511 O-518

A: The given series is 9+2-5-12-19-... This is arithmetic series, such that First term a=9 Common…

Q: Find the sum of the series (In 2)2 (In 3)3 1– In 2+ 3! +.. 2!

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Q: Check whether 301 is a term of the given series 5,11,17,23

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Q: In geometric sequence a1, a2, - --, an , if a4 = 1472 and a6 23552, then the common ratio is O 4 O 5…

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Q: Is an arithmetic series, S40 = 1900 and U40 = 106. Find the value of the first term and the common…

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Q: What is the value of c in the arithmetic series 4 + b + c + d + e + . . . if the sum of the first…

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Q: Consider the following sequence. 6, 18, 54, 162,    Find the sum to 10 terms. s10 = ? If the…

A: 6,18,54,162,.... Formula Sum of n terms Sn=a(1-rn)1-rSum of infinityS=a1-r

Q: 15 (k-50)

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Q: Provide the first 4 terms of the sequence {an} = n", where n ≥ 1 {an} 1 4 = 27 Question 2 What is…

A: The solutions to the given questions are given below

Q: 1. Which of the numbers does not fit into the series 10, 12, 28, 90, 368, 1840, 1112? * a. 368 b. 90…

A: topic - sequence and series

Q: Find the sum of the infinite geometric​ series, if it exists.   −12−4−4/3−4/9−

A: Explanation of the solution is given below...

Q: What is the sum of the geometric series in which a1 = 4, r = 3, and an = 324? Hint:  r ≠ 1, where…

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Q: 1. Find the next two numbers of the followin series: a) 31, 28, 31, 30, 31 b) 1, 2, 4, 7, 11 c) 3,…

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Q: Let, {an} = -5, 10, -20, 40, . . . , {bn} = 10, -5, -20, -35, . . . , and {cn} = -2, 1, - 1/2, 1/4 ,…

A: Given that, {an} = -5, 10, -20, 40, . . . First 6 terms of the sequence {an} are: -5, 10, -20, 40,…