Question

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is:

• A. 21
• B. 22
• C. 23
• D. 24

Answer 1

Answer: (C)

23

Answer 2

The correct answer is (C) : 23
a, A1, A2 …….. An, 100
Let d be the common difference of above A.P. then
$\frac{a+d}{100−d}=\frac{1}{7}$
⇒ 7a + 8d = 100 …(i)
and a + n = 33 …(ii)
and 100 = a + (n + 1)d
⇒$100=a+(34−a)\frac{(100−7a)}{8}$
⇒ 800 = 8a + 7a2 – 338a + 3400
⇒ 7a2 – 330a + 2600 = 0
$⇒a=10,\frac{260}{7}$
but
$a≠\frac{260}{7}$
∴ n = 23