The first and the last term of an A.P. are 17 and 350 respectively. If

1.	The first and the last term of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Answer» Given, First term, a₁ = 17 Last term, a_n = 350 = l And difference, d = 9 We know, a_n = a + (n – 1)d 350 = 17 + (n – 1) (9) 350 = 8 + 9n 342 = 9n n = 38 We know sum of n terms, S_n = \(\frac{n}{2}\)[a + l] S₃₈ = \(\frac{38}{2}\)[17 + 350] = 19 x 367 = 6973 Hence, number of terms, n = 38 sum of n terms, S_n = 6973

The first and the last term of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

Answer»

Given,

First term, a₁ = 17

Last term, a_n = 350 = l

And difference, d = 9

We know,

a_n = a + (n – 1)d

350 = 17 + (n – 1) (9)

350 = 8 + 9n

342 = 9n

n = 38

We know sum of n terms, S_n = \(\frac{n}{2}\)[a + l]

S₃₈ = \(\frac{38}{2}\)[17 + 350]

= 19 x 367 = 6973

Hence, number of terms, n = 38

sum of n terms, S_n = 6973