Question

Find the number of terms, n, of the arithmetic series given a = 21, an = 39, and Sn = 210.

Answer 1

The number of terms n is 7.

Explanation:

Given that:

First term a=21

nth term $a_{n}$=39

Sum up to n terms $S_{n}$=210

To Find:

The number of terms n in the arithmetic progression.

Formula to be used:

Sum up to n terms Sn is given by the expression

$S_{n} =\frac{n}{2} (a+a_{n} )$

Solution:

$S_{n} =\frac{n}{2} (a+a_{n} )\\\\210=\frac{n}{2}(21+39)\\\\210=\frac{n}{2}(60)=30n\\\\n=210/30=7$

Number of terms n in the given series is n=7