Question

The first and the last terms of an A. P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

Answer 1

let 'a' and 'd' are first term and common difference for an AP.

Number of terms of AP = n

last term = nth term = l

a = 17, d = 9 and l = 350

a + ( n - 1 ) d = 350

17 + ( n - 1 ) 9 = 350

( n - 1 ) 9 = 350 - 17

( n - 1 ) 9 = 333

n - 1 = $\frac{333}{9}$

n - 1 = 37

n = 37 + 1

n = 38

Therefore, number of terms in given AP = n = 38

Sum of n terms of AP = $S_n$

$S_n$ = $\frac{n}{2}$ ( a + l )

here n = 38

$S_{38}$ = $\frac{38}{2}$ [ 17 + 350 ]

= 19 $\times$ 367

= 6973