Question

the 8th term of an A P IS 37and its 12 th term is 57.find the AP

Answer 1

a(n)= a+(n-1)d
⇒a(8)= a+(8-1)d
⇒a+7d=37 --(1)

a(n)= a+(n-1)d
⇒a(12)= a+(12-1)d
⇒a+11d=57 --(2)

(2)-(1)
⇒a+11d-1-7d=57-37
⇒4d=20
⇒d=5

a=7d=37
⇒a+7(5)=37
⇒a+35=37
⇒a=2

The A.P is 2,7,12,17,22,.....

Answer 2

$\bold \red \star \: \large \underline{Given:-}$

${8}^{th} = a + 7d = 37. \\ \\ {12}^{th} = a + 11d = 57. \\ \\ \bold \red \star \: \large \underline{Answer:-}$

$\longrightarrow \: 2,7,12,17......$