Question

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

Answer 1

Let a be the first term and d be the common difference.Now,
a10 = 21⇒a + 9d = 21.. (1)
Now,
Sn = n/2[2a+ (n−1)d]
⇒S10 = 10/2(2a+9d)
⇒120 = 10a + 45d

⇒2a + 9d = 24 .....(2)
Subtracting (1) from (2) , we get
a = 3
Now,from (1),
we get9d = 21 − 3
⇒9d = 18⇒d = 2
Now,
nth term = a+(n−1)d
= 3+(n−1)2
= 3+2n−2
= 2n+1