# FIND TERMS OF A SEQUENCE

## About "Find terms of a sequence"

Find terms of a sequence :

To find the missing terms of the given sequence, first we have to check whether the given sequence is in arithmetic progression or geometric progression.

Let us see some example problems to  understand the above topic.

Example 1 :

Find the missing term of the following arithmetic progression.

2, ____, 26

Solution :

Let "x" be the second term.

In any arithmetic progression, common difference will be equal.

x - 2   =  26 - x

x - 2 + x  =  26 - x + x

2x - 2  =  26

2x -2 + 2  =  26 + 2

2x  =  28

Divide by 2 on both sides

2x/2  =  28/2

x  =  14

Hence, the missing term is 14.

Example 2 :

Find the next term of the following arithmetic progression.

5, 2, -1,- 4, .............

Solution :

Let "x" be the next term of the sequence

In any arithmetic progression, common difference will be equal.

-1 - 2   =  -4 - x

-3  =  -4 - x

-3 + x  =  -4 - x + x

-3 + x  =  -4

-3 + x + 3  =  -4 + 3

x  =  -1

Hence, the missing term is -1.

Example 3 :

Find the next term of the following geometric progression

2/5, _____, 18/125,..............

Solution :

Let "x" be the missing term of the sequence

In any geometric progression, common ratio will be equal.

x / (2/5)  =  (18/125)/x

5x/2  =  18/125x

Multiply by 125x on both sides

5x(125x) / 2  =  18

Multiply by 2 on both sides

625x  =  18 (2)

625x²  =  36

Divide by 625 on both sides

x²  =  36/625

x²  =  (6/25)²

x  =  6/25

Hence the second term of the above geometric progression is 6/25.

Example 4 :

Find the next term of the following geometric progression

5, 2, 4/5, 8/25, ..............

Solution :

Let "x" be the next term of the sequence

In any geometric progression, common ratio will be equal.

(8/25) / (4/5)  =  x / (8/25)

(8/25) x (5/4)  =  x (25/8)

40/100  =  25x/8

Multiply by 100 on both sides

40  =  (25x/8) 100

40  =  (2500x/8)

Multiply by 8 on both sides

40(8)  =  2500 x

Divide by 2500 on both sides

320/2500  =  x

x  =  32/250

x  =  16/125

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