If 5 + 9 + 13 + ... to n terms/7 + 9 + 11+ ..... to (n + 1) terms =17 / 16, then n = A. 8 B. 7 C. 10

Question

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

A. 8

 B. 7

C. 1000

D. 11

Answer 1

Correct answer is B. 7

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

Now, Sum of n terms

On cross multiplying we get, 

16n[3 + 2n] = 17n + 17[7 + n] 

⇒ 48n + 32n² = 119n + 17n² + 119 + 17n 

⇒ 48n + 32n² = 136n + 17n² + 119 

⇒ 15n² – 88n – 199 = 0

⇒ n = \(\frac{105}{15}\) = 7