Question

The 24th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.

Answer 1

$a_{24}=5+2a_8$ and $a_{11}=43$

we know nth of an A.P, $a_n=a+(n-1)d$ where
a = first term

d = common difference of A.P


therefore


a + (24 - 1) d = 5 + 2[ a + (8 - 1 ) d]


a + 23 d = 5 + 2a + 14d
23d-14d+a-2a
9d - a = 5 .......(1)


also
a + (11 - 1)d = 43
a + 10d = 43 .........(2)


solving 1 and 2 gives 19d = 48 $d=\frac{48}{19}$

from equation (1)
$9\left(\frac{48}{19}\right)-a=5$
$(9\times \frac{48}{19})-5=a$
$\frac{432-95}{19}=a$
$\frac{337}{19}=a$

hence nth tern would be $=\frac{337}{19}+(n-1)\frac{48}{19}$