Question

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

Answer 1

Answer:

11 is a good answer in this question

Answer 2

B. 7

Step-by-step explanation:

5+9+13...to n terms

S = n/2(10 + (n-1)4) = n/2 (10 +4n - 4) = n/2(6 + 4n) = n(3+2n) ----(1)

7+9+11+.....to(n+1)terms

S = n+1/2 (14 + (n+1-1)2) = (n+1)(n+7) -----------(2)

Now, we have n (3 + 2n) / (n+1)(n+7) = 17/16

  16n (3+2n) = 17(n² +8n +7)

  48n + 32n² = 17n² + 136n + 119

  15n²- 88n - 119 = 0

  15n² - 105n + 17n - 119 = 0

  15n (n - 7) +17 (n-7)= 0

  (15n + 17) (n-7) = 0

n is not a fraction. So we take n = +7

Option B is the answer.