Question

find the first and common difference of an ap whose t8=3 t12= 52​

Answer 1

let the first term and common difference of Ap be 'a' and 'd' respectively.

$t_{n}$ = a + (n-1)d

ATQ

$t_{8}$ = 3

==> a + (8-1)d = 3

==> a + 7d = 3 -----(i)

$t_{12}$ = 52

==> a + (12-1) d = 52

==> a + 11d = 52 ------(ii)

eqn (ii) - eqn (i), we get

4d = 49

d = 49/4

sub. d in eqn (i),

a + 7 * 49/4 = 3

==> a + 343/4 = 3

==> a = 3 - 343/4

==> a = 12 - 343/4

==> a = -331/4

Therefore, first term is -331/4 and common difference is 49/4.