The first term of an A.P. is 5, the common difference is 3 and the las

1.	The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
Answer» Given, a = 5 and d = 3 We know that, n^th term a_n = a + (n – 1)d So, for the given A.P. a_n = 5 + (n – 1)3 = 3n + 2 Also given, last term = 80 ⇒ 3n + 2 = 80 3n = 78 n = 78/3 = 26 Therefore, there are 26 terms in the A.P.

The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.

Answer»

Given,

a = 5 and d = 3

We know that, n^th term a_n = a + (n – 1)d

So, for the given A.P. a_n = 5 + (n – 1)3 = 3n + 2

Also given, last term = 80

⇒ 3n + 2 = 80

3n = 78

n = 78/3 = 26

Therefore, there are 26 terms in the A.P.