Question

Calculate S_24 for the arithmetic squence in which a_13= 1.9 and the common difference is d=3.7

A. -42.5
B. 42.6
C. -59.4
D. 1.2

Answer 1

D. 1.2

Explanation:

The sum of an arithmetic sequence is the product of the average term value and the number of terms.

The average term is often computed by averaging the first and last terms of the sequence. It can also be computed by averaging the middle two terms of the sequence (when there are an even number of terms, as here).

We are given a_13 is 1.9. We know that a_12 is 3.7 less, so is -1.8. Then the average of these two middle terms is ...

... (-1.8 + 1.9)/2 = 0.05

The product of this value and the number of terms (24) is ...

... 24·0.05 = 1.2 . . . . . the sum of 24 terms of the sequence