The 6th term of an arithmetic progression is 35 and the 13th term is 77. find the 20th term

20th term= 119

Step-by-step explanation:

Let the first term of AP be a

and common difference be d

nth term is given by,

= a+(n-1)d

6th term = 35

a+(6-1)d= 35

a+5d=35 (i)

13th term = 77

a+12d= 77(ii)

Now, equation (ii) - (i)

a+12d-(a+5d)= 77-35

a+12d-a-5d= 42

7d=42

d=6

Now, from equation (i)

a= 35-5d= 35-5(6)= 35-30 = 5

20th term= a+19d= 5+19(6)= 119