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Question

If A1,A2 be two arithmetic means between 13 and 124, then their values are
  1. 736,572
  2. 572,1772
  3. 1772,536
  4. 772,536


Solution

The correct option is C 1772,536
Here 13,A1,A2,124 will be in A. P., then A113=124A2A1+A2=38              .....(i)
Now, A1 is a arithmetic mean of 13 and A2,
we have 2A1=13+A2 2A1A2=13  ......(ii)
From (i) and (ii), we get, A1=1772 and A2=536.
Aliter : As we have formula Am=a+m(ba)n+1
where n = 2, a=13,b=124
 A1=13+7/243=1772
A2=13+14/243=1072=536

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