Question

If the 10th term of an A.P. is 21 and the sum of its first ten terms is 120 ,find its nth term.

Answer 1

Hey!!


Let first term be a

and common difference be d


A / q

a10 = 21

=> a + 9d = 21 ------- ( 1 )

And


S10 = 120

=> 10 / 2 [ 2a + 9d ] = 120

=> 5 [ 2a + 9d ] = 120

=> 2a + 9d = 24 ---------- ( 2 )


On solving ( 1 ) and ( 2 )


a + 9d = 21

2a + 9d = 24

( - )---( - )--( - )
____________

=> - a = - 3

=> a = 3


From ( 1 )

a + 9d = 21

=> 3 + 9d = 21

=> 9d = 21 - 3

=> 9d = 18

=> d = 2


We know that nth term


an = a + ( n - 1 )d

=> an = 3 + ( n - 1 ) 2

=> an = 3 + 2n - 2

=> an = 2n + 1.




Hope it helps!