Question

Find the sum of the first 47 terms of the following series, to the nearest integer.
13, 18, 23, ...

Answer 1

Answer:

The sum of the first 47 terms of the given series = 6016

Step-by-step explanation:

Given the sequence

13, 18, 23, ...

An arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

$18-13=5,\:\quad \:23-18=5$

As the difference between all the adjacent terms is the same.

so

$d=5$

$a_1=13$

Arithmetic sequence sum formula

$n\left(a_1+\frac{d\left(n-1\right)}{2}\right)$

Put the values

$d=5$

$a_1=13$

$n=47$

$=47\left(13+\frac{5\left(47-1\right)}{2}\right)$

$=47\left(13+\frac{5\left(47-1\right)}{2}\right)$

$=47\left(13+115\right)$

$=47\cdot \:128$

$=6016$

Thus, the sum of the first 47 terms of the given series = 6016