Question

What is the sum of the arithmetic sequence 151, 137, 123, ..., if there are 26 terms?

Answer 1

what is the difference between these terms ? how you can write a general formula of these terms ?

Answer 2

the sequence is arithmetic, so we can find the common difference by subtracting any term - the previous term

for instance, take the 137, and subtract by the previous term, 151 ---> 137 - 151 = -14

this is your d-value

the first term, a1, = 151
there are 26 terms, so n = 26

plug into

\[S_{n}=\frac{ n }{ 2 }(2a_{1}+(n-1)d)\]