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.
Given,
a = 5, last term, l = an = 80
Common difference, d = 3
We know, an = a + (n – 1)d where a is first term or a1 and d is common difference and n is any natural number
∴ an = 5 + (n – 1)3
⇒ an = 5 + 3n – 3
⇒ an = 3n + 2
To find total terms of the A.P., put an = 80 as 80 is last term of A.P.
∴ 3n + 2 = 80
⇒ 3n = 80 – 2
⇒ 3n = 78
⇒ n = 26
Hence, there are total 26 terms in the given A.P.