Question

What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

Answer 1

Since the sequence is arithmetic, we have an expression of the form:
 $an = a1 + d (n-1)$
 Where,
 a1: first term of the sequence
 d: common difference
 n: number of terms
 We look for the common difference:
 $d = 22-15 = 15-8 = 7 d = 7$
 Then, setting values we have:
 $a26 = 8 + 7 * (26-1) a26 = 183$
 Then, the sum of the terms is:
 $Sn = ((a1 + an) / (2)) * n$
 Substituting values:
 $Sn = ((8 + 183) / (2)) * 26 Sn = 2483$
 Answer:
 the sum of the arithmetic sequence 8, 15, 22 is:
 Sn = 2483