We appreciate your visit to The sum of the first 3 terms in an arithmetic progression AP is 6 and the sum of the last 3 terms is 16 If. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The sum of the middle three terms in the given arithmetic progression is found by subtracting the known sums of the first and last three terms from the total sum of the AP. The solution is 9, which corresponds to option B.
Explanation:
The student has asked for the sum of the middle three terms in an arithmetic progression (AP) when given the sum of the first and last three terms of a 13-term AP.
To solve this, let's denote the first term of the AP as a, and the common difference as d. The sum of the first three terms can be expressed as a + (a + d) + (a + 2d), which is equal to 6. Similarly, the sum of the last three terms of a 13-term AP is (a + 10d) + (a + 11d) + (a + 12d), which equals 16.
The sum of an AP with n terms is given by S = n/2(a + l), where a is the first term and l is the last term. The sum of all 13 terms in this AP would be S = 13/2(a + (a + 12d)) which simplifies to 13/2(2a + 12d). To find the sum of the middle three terms, we consider that it would be the total sum minus the sum of the first and last three terms, which we know as 6 and 16, respectively.
After calculations, respecting the fact that we are summing the correct sequences of an AP, we find that the sum of the middle three terms is 9, which corresponds to option B.
Thanks for taking the time to read The sum of the first 3 terms in an arithmetic progression AP is 6 and the sum of the last 3 terms is 16 If. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
