Question

If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, find the sum of n terms.

Answer 1

In the given problem, we need to find the sum of n terms of an A.P. Let us take the first term as a and the common difference as d.

Here, we are given that,

So, as we know the formula for the sum of n terms of an A.P. is given by,

Where; a = first term for the given A.P.

d = common difference of the given A.P.

n = number of terms

So, using the formula for n = 7, we get,

Further simplifying for a, we get,

Also, using the formula for n = 17, we get,

Further simplifying for a, we get,

Subtracting (3) from (4), we get,

Now, to find a, we substitute the value of d in (3),

Now, using the formula for the sum of n terms of an A.P., we get,

Therefore, the sum of first n terms for the given A.P. is.