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The mean of five numbers in AP is $89$ . The product of first and last terms is $7885$ . The arithmetic mean of first, third and fifth term is

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83

86

89

90

answer is C.

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Detailed Solution

Given, the mean of five numbers in AP is

89

and the product of first and last terms is

7885

.
Let the terms of the given AP be,

(a - 2 d), (a - d), a, (a + d), (a + 2 d)

.
Now, according to the given condition,

\frac{(a - 2 d) + (a - d) + a + (a + d) + (a + 2 d)}{5} = 89

\Rightarrow \frac{5 a}{5} = 89

⇒

a = 89

The arithmetic mean of 1st, 3rd and 5th terms can be given by,

\frac{(a - 2 d) + a + (a + 2 d)}{3}

= a

Therefore, the arithmetic mean of first, third and fifth term is

a = 89

.
Hence, the correct option is 3.

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