Question

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

Answer 1

Hi ,

let a and d are first term and common

difference for an AP.

number of terms of AP = n

last term = nth term = l = an

a = 17 , d = 9 ,

l = 350

a + ( n - 1 ) d = 350

17 + ( n - 1 ) 9 = 350

( n - 1 ) 9 = 350 - 17

( n - 1 ) 9 = 333

n - 1 = 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 = Sn

Sn = n /2 ( a + l )

here n= 38

S38 = 38 / 2 [ 17 + 350 ]

= 19 × 367

= 6973

I hope this helps you.

Answer 2

Answer:

Let a= 17

an = 350

d= 9

an = a+(n-1) d

350 = 17 + (n-1) 9

333 = 9n-9

342 = 9n

n = 38

Therefore,there are 38 terms

Sum:

Sn = n/2 (2a+ (n-1) d)

= 19 (34 + 333)

= 19 (367)

= 6973

Therefore, the sum is 6973

Hope it helps...