If 10th term is 21 and sum of its first 10 terms is 120. Find nth term

1.	If 10th term is 21 and sum of its first 10 terms is 120. Find nth term.
Answer» Thanks Let’s consider a to be the first term and d be the common difference.And we know that, sum of first n terms is:Sn\xa0= n/2(2a + (n − 1)d)\xa0and nth\xa0term is given by: an\xa0= a + (n – 1)dNow, from the question we have S10\xa0= 120⟹\xa0120 = 10/2(2a + (10 − 1)d)⟹\xa0120 = 5(2a + 9d)⟹ 24 = 2a + 9d\xa0…. (1)Also given that, a10\xa0= 21⟹\xa021 = a + (10 – 1)d⟹\xa021 = a + 9d\xa0…. (2)Subtracting (2) from (1), we get24 – 21 = 2a + 9d – a – 9d⟹a = 3Now, on putting a = 3 in equation (2), we get3 + 9d = 219d = 18d = 2Thus, we have the first term(a) = 3 and the common difference(d) = 2Therefore, the nth\xa0term is given by an = a + (n – 1)d = 3 + (n – 1)2= 3 + 2n -2= 2n + 1Hence, the nth\xa0term of the A.P is (an) = 2n + 1.

Discussion