Question

the 8th term of an ap is 32and its 12 term is 52.find ap​

Answer 1

the first term is -3 and the common difference is 5

Answer 2

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GIVEN :

The 8th term of an AP is 32 .

The 12th term of an AP is 52.

TO FIND :

The AP

ANSWER :

The general term,tn =

$tn = a + (n - 1)d$

where n is the nth term.

a is the first term.

d is the common difference.

t8 = a + ( 8 - 1) d

a + 7d = 32 ________(1)

t12 = a + (12 - 1) d

a + 11d = 52 _________(2)

Subtract (1) & (2) ,

(2) => a + 11d = 52

(1) => a + 7d = 32

(-) (-) (-)

_________________

4d = 20

d = 20/4

d = 5 .

Substitute the value of d = 5 in equation (1),,,,

(1) => a + 7 (5) = 32

a + 35 = 32

a = 32 - 35

a = -3

The general form of an AP is ,,,,,

$ap \: = (a) + (a + d) + (a + 2d) + ..$

AP = -3 + ( -3 + 5) + ( -3 + 2 ×5) + ....

AP = -3 + 2+ 7 +....

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