If (5+9+13+...n)7+9+11+...(n+1)=1716 , then n is equal to
7
6
9
None of these
Step 1. Find the value of n:
Given, (5+9+13+...n)7+9+11+...(n+1)=1716
Take (5+9+13+…n)
Here, a=5 and d=4
⇒S1=n210+(n-1)4=n26+4n
Now take, 7+9+11+…(n+1)
Here, a=7 and d=2
⇒S2=(n+1)2(14+2n)
Step 2. Divide S1 by S2, we get
(5+9+13+...n)7+9+11+...(n+1)=1716
⇒ S1S2=1716
⇒ n2(6+4n)(n+1)2(14+2n)=1716
⇒ 15n2-88n-119=0
⇒15n(n-7)+17(n-7)=0
⇒ (n-7)(15n+17)=0
⇒ n=7,-1715
n cannot be negative.
∴n=7
Hence, option (A) is correct.