Question

The first and the last terms 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 1

Answer:

There are 38 number of terms and sum of these terms are 6973.  

Step-by-step explanation:

Given :  

First term, a = 17, last term , l = 350, common Difference , d = 9

By using the formula , l = a + (n - 1) d

350 = 17 + (n - 1) 9

350 - 17 = 9 (n -1)

333/9 = n - 1

37 = n - 1

n = 37 + 1

n = 38

By using the formula ,Sum of nth terms , Sn = n/2(a + l)

Sn = 38/2(350 + 17)

Sn = 19 (367)  

Sn = 6973

Hence, there are 38 number of terms and sum of these terms are 6973.  

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Answer 2

GIVEN :

First term of an A.P = a = 17

Last term of an AP = n = 350

Common difference between them = d = 9

In an AP an = a + (n-1)d.

350 = 17 + ( n-1)9

350 = 17 + 9n - 9

350 = 8 + 9n

350 - 8 = 9n

9n = 342

n = 342

n = 38

There are 38 terms in the AP.

In an AP Sum of the terms = n/2 ( a + an ).

An = 38/2 ( 17 + 350 )

= 19 ( 357 )

= 6973

Therefore, the sum of the terms in AP is 6973.