Find the sum of a 22-term arithmetic sequence where the first term is 56 and the last term is -28

Frida Faulkner

Frida Faulkner

Answered question

2022-09-06

Find the sum of a 22-term arithmetic sequence where the first term is 56 and the last term is -28

Answer & Explanation

Jaylen Mcmahon

Jaylen Mcmahon

Beginner2022-09-07Added 16 answers

The sequence is {56+(n-1)d}, 2 = 1, 2, 3, ...,22, wher d is the common difference.
The last term (n=22) is - 28 = 56 + 21 d ,
So, d = - 82 21 = - 4 .
The sum = ( 22 ) ( 56 ) + ( d + 2 d + 3 d , ... + 21 d ) = 1232 - ( 21 ) ( 22 2 ) ( - 4 ) . using 1 + 2 + 3 ... + n = n ( n + 1 ) 2
The sum simplifies to 308.

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