Question

The 8th term of ap is -23 and it's 12th term is -39 find the ap

Answer 1

Answer:

let, a and d be the 1st term and common difference of AP

1.

8th term of AP =-23

or, a+7d = -23.......(1)

2.

12th term of AP =-39

or, a+11d =-39......(2)

subtracting equation 1 from 2

a+11d=-39

-a-7d=23

4d=-16

d=-4

so,,,,

a=5

now...

5,1,-3,-7,-11 are in AP

Answer 2

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GIVEN :

The 8th term of an AP is - 23 .

The 12th term of an AP is -39.

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 = -23 ________(1)

t12 = a + (12 - 1) d

a + 11d = -39 _________(2)

Subtract (1) & (2) ,

(2) => a + 11d = -39

(1) => a + 7d = -23

(-) (-) (+)

_________________

4d = -16

d = -16/4

d = - 4

Substitute the value of d = -4 in equation (1),,,,

(1) => a + 7 (-4) = -23

a - 28= -23

a = 28 - 23

a = 5

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

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

AP = 5 , ( 5 - 4) , ( 5 + 2 × -4 ) ,....

AP = 5 , 1 ,- 3 , ...

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