The third and sixth terms of a series in A.P are 13 and 31 respectively. Find 20th term.

Q. The third and sixth terms of a series in A.P  are 13 and 31 respectively. Find 20th term.

Solution:

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

Given, third term=t₃=13

⇒a+(3-1)*d=13

⇒a+2d=13...................(i)

and sixth term=t₆=31

⇒a+(6-1)*d=31

⇒a+5d=31...............(ii)

(ii)-(i)⇒(a+5d)-(a+2d)=31-13

⇒a+5d-a-2d=18

⇒a-a+5d-2d=18

⇒0+3d=18

⇒3d=18

⇒d=18÷3

⇒d=6

Substituting the value of d=6 to the equation (i),we get

(i)⇒a+2*6=13

⇒a+12=13

⇒a=13-12

⇒a=1

20th term=t₂₀=a+(20-1)*d

=1+19*6

=1+114

=115.