Question

If $\frac{5+9+13+...tonterms}{7+9+11+...to(n+1)terms}=\frac{17}{16},$then n =

(a) 8

(b) 7

(c) 10

(d) 11

Answer 1

Here, we are given,

We need to find n.

So, first let us find out the sum of n terms of the A.P. given in the numerator. Here we use the following formula for the sum of n terms of an A.P.,

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

d = common difference of the given A.P.

n = number of terms

Here,

Common difference of the A.P. (d) =

Number of terms (n) = n

First term for the given A.P. (a) =

So, using the formula we get,

Similarly, we find out the sum of terms of the A.P. given in the denominator.

Here,

Common difference of the A.P. (d) =

Number of terms (n) = n

First term for the given A.P. (a) =

So, using the formula we get,

Now substituting the values of (2) and (3) in equation (1), we get,

Further solving the quadratic equation for n by splitting the middle term, we get,

So, we get

Or

Since n is a whole number, it cannot be a fraction. So,

Therefore, the correct option is (b).