Question

the 8th term of an ap 37is and 12th term is 57 find ap

Answer 1

given a8 = 37

a12 = 57

a+7d = 37----1

a+11d = 57----2

now 2-1

4d = 20

d = 5

put value of d in 1

a+7*5 = 37

a= 37-35 = 2


thus a.p will be 2,7,12,17,22,27.....

Answer 2

Given:

$a+7d= 37 \\\\ a+11d= 57$

To find:

Ap series=?

Solution:

$\to a+7d= 37. . . . . . . . . .(a)\\\\ \to a+11d= 57. . . . . . . . .(b)$

Equation (a) we multiply by 11 and in equation (b) we multiply by 7 then subtract the equation:

$\to 11a+77d= 407 \\\\ \to 7a+77d= 399\\ \ \\\ \ - \ \ \ \ \ \ - \\\ \to 4a= 8\\\\\to a= \frac{8}{4}\\\\\to a= 2$

put the value of "a" in equation (b):

$\to 2+11d=57\\\\\to 11d=57-2\\\\\to 11d= 55\\\\\to d=\frac{55}{11}\\\\\to d= 5$

series:

$\to a, a+d,a+2d. . . . .\\\\\to 2, 7, 12,17,22,27. . . . . .$