# FIND THE INDICATED TERMS OF THE ARITHMETIC SEQUENCE

Find the Indicated Terms of the Arithmetic Sequence :

In this section, let us see some example problems of finding the missing term from the given information.

To find the sum of an arithmetic series, we use the formulas give below.

Sn  =  (n/2) [a + l] (or)

Sn  =  (n/2) [2a + (n - 1)d]

nth term of arithmetic progression :

an  =  a + (n - 1)d

Total number of terms :

n  =  [(l - a)/d] + 1

a = first term, d = common difference, n = number of terms and l = last term.

## Find the Indicated Terms of the Arithmetic Sequence - Examples

Question 1 :

Given an = 4, d = 2, Sn = -14 find n and a

Solution :

an = 4

a + (n - 1) d  =  4

a + (n - 1)2  =  4

a + 2n - 2  =  4

a + 2n  =  6

a  =  6 - 2n  ---(1)

Sn  =  -14

Sn  =  (n/2) [2a + (n - 1)d]

-14  =  (n/2) [2a  + (n - 1)2]

-14  =  (n/2) [2a  + 2n - 2] ----(2)

By applying the value of a in (2), we get

-14  =  (n/2)[2(6 - 2n) + 2n - 2]

-28  =  n[12 - 4n + 2n - 2]

-28  =  n[10 - 2n]

-28  =  10n - 2n2

2n2 - 10n - 28  =  0

Dividing it by 2, we get

n2 - 5n - 14  =  0

(n - 7) (n + 2)  =  0

n  =  7  or n = -2 (not admissible)

By applying the value of n in (1), we get

a  =  6 - 2(7)

a  =  6 - 14

a  =  -8

Hence the values of a and n are -8 and 7 respectively.

Question 2 :

Given a = 3, n = 8, Sn = 192 find d

Solution :

Sn  =  192

Sn  =  (n/2) [2a + (n - 1)d]

192  =  (8/2) [2(3) + (8 - 1)d]

192  =  4 [6 + 7d]

192/4  =  6 + 7d

48  =  6 + 7d

48 - 6  =  7d

7d  =  42

d  =  42/7  =  6

Hence the value of d is 6.

Question 3 :

Given l = 28 , S = 144 , and there are total 9 terms. Find a

Solution :

Let "l" be the last term or nth term of the series.

l  =  tn  =  28

tn  =  a + (n - 1)d

a + (9 - 1)d  =  28

a + 8d  =  28 ----(1)

S9  =  144

Sn  =  (n/2) [2a + (n - 1)d]

(n/2) [2a + (n - 1)d]  =  144

(9/2) [2a + 8d]  =  144

[2a + 8d]  =  144  (2/9)

2a + 8d  =  32

a + 4d  =  16  ------(2)

(1) - (2)

a + 8d  =  28

a + 4d  =  16

(-)     (-)    (-)

---------------

4d  =  12

d  =  3

By applying the value of d in (1), we get

a + 8(3)  =  28

a + 24  =  28

a  =  28 - 24  =  4

Hence the first term is 4. After having gone through the stuff given above, we hope that the students would have understood, find the indicated terms of the arithmetic sequence.

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