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Sum of n Terms

The common di...

Question

The common difference d of the A.P in which $T_{7} = 9$ and $T_{1} T_{2}$ has least value

\frac{33}{2}

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\frac{5}{4}

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\frac{33}{20}

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None of these

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Solution

The correct option is A $\frac{33}{20}$
$T_{7} = 9 a + 6 d = 9 a = 9 - 6 d T_{1} T_{2} = (9 - 6 d) (9 - 5 d) = 30 d^{2} - 99 d + 81 = 30 (d^{2} - 99 / 30) + 81 = 30 (d^{2} - 33 / 10 + 33^{2} / 20^{2}) + 81 - 30 \times 33^{2} / 20^{2} = 30 {(d - 33 / 20)}^{2} - 270 / 400$
To make it $l e a s t$
$d - 33 / 20 = 0 d = 33 / 20$

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520

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