Question

The 8th and 12th terms of an AP are 17 and 25 respectively. Find its 20th term

Answer 1

Solution :-

The 8th and 12th terms of an AP are 17 and 25 respectively.

Therefore,

8th term = a + 7d = 17 ...eq( 1 )

12th term = a + 11d = 25. ...eq( 2 )

Subtract eq( 2 ) from eq( 1 )

a + 11d - ( a + 7d) = 25 - 17

a + 11d - a - 7d = 8

11d - 7d = 8

4d = 8

d = 8/4 = 2

Thus, The value of d is 2

Now,

Subsitute the value of d in eq ( 1 ) , we get :-

a + 7( 2 ) = 17

a + 14 = 17

a = 17 - 14 = 3

Thus, The value of a is 3

Now,

we have to find the 20th term of an AP

Therefore,

As we know that,

an = a + (n - 1 )d

a20 = 3 + ( 20 - 1 )2

a20 = 3 + ( 19)2

a20 = 3 + 38

a20 = 41

Hence, The 20th term of an AP is 41 $.$