# FROM THE GENERAL TERM FIND THE SUM OF SERIES

In this section, you will learn how to find the sum of the series and its general term, if its sum to n terms is given.

Example :

If the sum of the first n terms of an AP is 4n - n2  what is the first term (that is S)? what is the sum of first two terms ? what is the second term ? similarly find the 3rd, the 10th and the nth terms.

Solution :

Given that :

Sn  =  4 n - n2

By applying n = 1, we get the first term. By applying n = 2, we get the sum of first two terms.

 n = 1S1  =  4(1) - 12  =  4 - 1S1  =  3 n  =  2S2  =  4(2) - 22  =  8 - 4S2  =  4

First term (a)  =  3,

Sum of first two term  S2  =  a + a + d  =  4

2a + d  =  4

By applying the value of a, we get

2(3) + d  =  4

d  =  4 - 6

d  =  -2

By using the values of a and d, let us find the 3rd, the 10th and the nth terms.

a  =  3 and d  =  -2

an  =  a + (n - 1) d

 a3  =  a + 2d  =  3 + 2(-2)  =  3 - 4a3  =  -1 a10  =  a + 9d  =  3 + 9(-2)  =  3 - 18a3  =  -15

nth term :

an  =  a + (n - 1) d

an  =  3 + (n - 1) (-2)

an  =  3 - 2n + 2

an  =  5 - 2n

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