Question

The 17th 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

Let 'a' be the first term & 'd' be the common difference

As/q

=2() +5

a+16d = 2 (a+7d)+5

=> a+16d = 2a +14d +5

=> 2a-a+14d-16d=-5

=> a-2d = - 5 ----------- (i)

now,

=43

=> a+10d= 43 --------(ii)

subtracting (i) frm (ii)

a+10d -a +2d=43 - (-5)

=> 12d =48

=> d = 4

putting d=4 in eq. (ii)

a+10 $\times$ 4 = 43

=> a = 43-40= 3

now,

nth term, $a_n=a+(n-1)d$

. = 3+(n-1)4

. = 3+4n-4

. = 4n -1

hence, its nth term= 4n-1