The 3rd and 6th terms of a series in A.P. are 13 and 31 respectively. Find 20th term.

Q. The 3rd and 6th terms of a series in A.P. are 13 and 31 respectively. Find 20th term.

Solution:

Let us assume that first term=a, common difference=d.

Given,

3rd term=t₃=13

⇒a+(3-1)d=13 (by the formula tₙ=a+(n-1)d)

⇒a+2d=13……………..(i)

and,

6th term=t₆=31

⇒a+(6-1)d=31

⇒a+5d=31………………(ii)

(ii)-(i)⇒(a+5d)-(a+2d)=31-13

⇒3d=18

⇒d=18/3

⇒d=6

Now substituting the value of d to the equation (i)

(i)⇒a+2*6=13

⇒a+12=13

⇒a=13-12

⇒a=1

So, 20th term=t₂₀=a+(20-1)d

=1+19*6

=1+114

=115