FIND TERMS OF A SEQUENCE

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

Add x on both sides,

x - 2 + x  =  26 - x + x 

2x - 2  =  26

Add 2 on both sides

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

Add x on both sides,

-3 + x  =  -4 - x + x

-3 + x  =  -4

Add 3 on both sides,

-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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