Our author Strogatz shows us something surprising about sums of consecutive counting numbers (integers), starting from 1. What is The sum of the first 6 consecutive integers? The sum of the first 7 consecutive integers? The sum of the first 2625 consecutive integers?

Q: What’s next in this number sequence: 7, 9, 22, 72, 296, x?

A: Given sequence is,7,9,22,72,296, x?We have to find value of x.

Q: .What is the sum of all odd numbers between 1 to 50?

A: 10. The odd numbers between 0 to 50 are 1, 3, 5, 7, …., 49. Here, First term a=1, last term l=49.…

Q: What is a formula to calculate the sum of the first n positive integers? Could you explain why this…

A: Obtain the sum of first n positive integers as follows.The general formula to calculate the sum of…

Q: A license plate must contain 2 numerical digits followed by 2 letters. If the first digit cannot be…

A: Given 1. A license plate must contain 2 numerical digits followed by 2 letters. 2. the first digit…

Q: What is the next three numbers in the sequence: 2,5,10,17,26,37,50?  What formula can be used to…

A: Consider the given series, 2,5,10,17,26,37,50 Obtain a pattern in the series as follows.…

Q: How many ways can the top four cash prices be awarded in a lottery that sold 150 tickets if each…

A: here given scenario is with replacement ,

Q: The Knightrola Lottery has been updated to allow choosing 6 numbers out of 63 on a $1 ticket.…

A: Cost of 1 lottery ticket is $1. Total number in the lottery are 63. Total selected number for 1…

Q: Our author Strogatz shows us something surprising about sums of consecutive odd counting numbers,…

A: Here we have to find the sum of consecutive odd numbers.

Q: Prove: The sum of an odd number of odd numbers must be odd.

A: Let us prove this by induction, that if n is odd and a1,a2,. . .. .an are odd, then ∑i=1nai is odd.…

Q: find a rule which describes the given numbers in the sequence 2. 1.1/8, 1/27, 1/64, 1/125..

A: Here is the solution:

Q: 2 letter sequences can be formed from the 8 letters in theword “sequence”?

A: Given, A letter = [ s,e,q,u,e,n,c,e] Number of letters = 8 By using  permutation and combination,…

Q: In the past, a local telephone number in a country consisted of a sequence of three letters followed…

A: The telephone numbers consist of sequences of 2 letters followed by 5 digits and 3 letters are…

Q: A man has time to play roulette 5 times. He wins or loses $ 1000 in every game. The man starts with…

A: Given information: Wins or loses per game = $1000

Q: sequence

A:

Q: How would you classify the sequence 28, 21,15, 10,6, ....? .......

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Q: Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number. 1.…

A: Here is a rule to a  list  of numbers  Each  number  is  4 less than  3 timesthe    previous number.…

Q: A license plate must contain 2 numerical digits followed by 3 letters. If the first digit cannot be…

A: Consider a license plate which has to contain 2 numerical digits and followed by 3 letters. The…

Q: What is the next number in the sequence: 1, 5, 35, 385, 6545, ... ?

A: The second number is obtained by multiplying the first number by 5. The third number is obtained by…

Q: A company has been selling 600 items every month at $ 720 each. However, for each $ 40 rebate…

A: The given data is: A company has been selling 600 items every month at $720 If a rebate of $40 is…

Q: How many terms are in the sequence:2, 6, 18, ….. 3188646?

A:

Q: Find the 9th term for the sequence of positive 3 digit numbers that are multiples of 5.

A: We have to find the 9th term for the sequence of positive 3 digit numbers that are multiples of 5…

Q: What is the sum of the first 150 positive integers?

A:

Q: What is the sum of all 13-digit numbers?

A: What is the sum of all 13-digit numbers?

Q: How many ways are there to choose three different numbers each between one and a hundred so that…

A: There can be two possibilities only 1) All the three numbers are even. 2) One number is even and two…

Q: What is the sum of number 10 to 40?

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Q: What is the sum of the first 200 positive integers?

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Q: what is the sequence of positive whole numbers

A: To find the sequence of positive while number.

Q: 2. What is the smallest sum that can be obtained by adding a positive number and its reciprocal?

A:

Q: Find the sum of the even integers between 35 and 49. The sum is ...

A:

Q: If a class of children is separated into groups of 5 children, 2 children will be left over. If the…

A: Let the number of children in the class is N. 1. It is given that when the children are seperated…

Q: What is the sum of the first 100 nonnegative integers?

A:

Q: What is the 15th number in the sequence 4, 8, 12, 16…?

A: Given that: A sequence: 4, 8, 12, 16, ....

Q: What is the 15th number in the sequence 3, 11, 19, 27…?

A:

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a. 3+2n

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Q: A boy gets 3 marks for each correct sum and loses 1 mark for each incorrect sum. He does 25 sums and…

A: Simple equation

Q: What is the smallest sum possible sum of 25 consecutive positive integers which s a perfect square?

A: Let's take the 25 consecutive positive numbers as an Arithmetic Progression with first term a.…

Q: Simplify the series of additions and subtractions

A: To simplify: the below series of additions and subtractions.

Q: Find the sum of all two digit odd multiples of 3.

A:

Q: Here is a sequence of numbers: 75, 34, 94, 81, 43, 106, 87, 52, 118, 93, 61, 130, ... Give the next…

A:

Q: B. You are instructed to subtract 4 points from each score and find the sum of the resulting values.…

A: We are asked to express a summation notation for given words

Q: What is the sum of the first 4 prime numbers greater than 35?

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Q: Susan's bioloy class begins with 1225 students. If 5/7 will finish the course and 2/25 of those get…

A: GivenTotal number of students is 1225.

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a = 3 + 2n

A:

Q: What is the sum of the first 9,000 positive integers

A: topic - arithmetic sequence answer is 40504500

Q: 2 3 4 5 1'2' 4'8'

A: topic - formula for sequence

Q: Find the sum of all Integers between 84 and 719 which are multiple of 5

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Q: If the sum of n successive odd natural numbers starting from 3 is 48 , Find the value of n

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Q: A gum ball machine had 7 red and 5 yellow gum balls left. You put pennies until you empty the…

A:

Q: Find the sum of the integers between301 and 400 inclusive that are multiples of 4.

A: