Question

The sum of first term and fifth term of an ap is 26 and the product of the second term with fourth term is 160. find the sum of first 7 terms of this ap.

Answer 1

Here's your answer hope it helps......:-)

Answer 2

Sum of first 7 terms of this AP is 112.

Solution:

Let us consider first term in series = A

$5^{th}$ term =  A + 4D

Product of $2^{nd}$ term of series = A + D  

$4^{th}$term = A + 3D  

Sum = A + A + 4D = 2A + 4D = 26  

Product of (A + D) (A + 3D) = 160

Now to find the value of A and D:

2A + 4D = 26

A+2D=13  

Substituting value of A+2D=13 in (A + D)(A + 3D) = 160 we get  

(13 – 2d + 3d)(13 – 2d + d) = 160  

After solving we get

(13 – D)(13 + D) = 160

$\begin{array}{l}{13^{2}-D^{2}=160} \\ {169-160=D^{2}} \\ {D=3}\end{array}$

Putting the value of d in A+2D=13 we get  

$A + 2 \times 3 = 13$

A = 7

Sum of first seven term = $\bold{\frac{n}{2}(2 A+(n-1) D)=\frac{7}{2}(14+18)=112}$