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Sum of n Terms

If an A.P., i...

Question

If an A.P., is $a_{7} = 9$ , if $a_{1} . a_{2} . a_{7}$ is least, the common difference is

A

13 / 20

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B

23 / 20

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C

33 / 20

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D

43 / 20

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Solution

The correct option is C $33 / 20$
$a_{7} = a + 6 d$ (General term in AP : $a_{r} = a + (r - 1) d)$
$= 9$
$a = 9 - 6 d$
$f (d) = a_{1}, a_{2}, a_{6}$
$= (9 - 6 d) (9 - 6 d + d) (9 - 6 d + 6 d)$
$\frac{d}{d (d)} (f (d))$ minima
$\Rightarrow 9 [(- 6) (9 - 5 d) + (9 - 5 d) - 5] = 0$
$d = \frac{99}{60} = \frac{33}{20}$
option C is correct.

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