What is the sum of the arithmetic sequence 4, 11, 18 …, if there are 26 terms?

Sariah Mcguire 2022-10-25 Answered
What is the sum of the arithmetic sequence 4, 11, 18 …, if there are 26 terms?
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Answers (1)

DoryErrofbi
Answered 2022-10-26 Author has 12 answers
This sequence can be written as:
a n + 1 = a n + 7
n [ 0 , 26 ] (for all n from 0 to 26, inclusive)
with a 0 = 4 .
You can also write this as:
n = 1 26 7 n - 3
...which is easier to solve, even by hand.
4 + 11 + 18 + ...
= ( 7 ( 1 ) - 3 ) + ( 7 ( 2 ) - 3 ) + ( 7 ( 3 ) - 3 ) + ...
= 7 ( 1 ) + 7 ( 2 ) + 7 ( 3 ) + ... - 3 - 3 - 3 - ...
= 7 ( 1 + 2 + 3 + ... + 26 ) - 3 ( 26 )
= 7 ( 26 27 2 ) - 78
= 7 ( 13 27 ) - 78
= 7 ( 3 27 + 10 27 ) - 78
= 7 ( 351 ) - 78
= 2457 - 78
= 2379
So, in general:
n = 1 N a n ± b = a 2 n ( n + 1 ) ± b n
7 2 ( 26 27 ) - 3 26 = 2379
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