Question

The 8th term of an AP is 37 and 12th term is 57. Find the AP.​

Answer 1

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GIVEN :

The 8th term of an AP is 37 .

The 12th term of an AP is 57.

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 = 37 ________(1)

t12 = a + (12 - 1) d

a + 11d = 57 _________(2)

Subtract (1) & (2) ,

(2) => a + 11d = 57

(1) => a + 7d = 37

(-) (-) (-)

_________________

4d = 20

d = 20/4

d = 5 .

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

(1) => a + 7 (5) = 37

a + 35 = 37

a = 37 - 35

a = 2

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

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

AP = 2 ,( 2 + 5) , ( 2 + 2 ×5) , ....

AP = 2 , 7, 12,....

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