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Home » The first and the last term of an A.P are and respectively. If the common difference is , how many terms are there and what is their sum?
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?
Arithmetic Progressions | CBSE | Class 10 | Exercise 9.6 | Maths | RD Sharma
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?

Given,

In an A.P first term (a) =17 and the last term (l) of A.P. =350

And, the common difference (d) of A.P. =9

As we know that,

{{a}_{n}}=a+\left( n-1 \right)d

so, by substitution,

{{a}_{n}}=l=17+\left( n-1 \right)9=350

17+9n-9=350

9n=350-8

n=342/9

n=38

So, the sum of all the term of the A.P is denoted by

{{S}_{n}}=n/2\left( a+l \right)

=38/2(17+350)

=19(367)

=6973

Therefore, the sum of 38 terms of the A.P is 6973.

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