Let a 1- a 2- a 3- - be an arithmetic progression with npn-zero common difference- It is given that - i -412 a i -63 and a k -7 for some k- Then the value of k isA- 6B- 7C- 8D- 9

The correct option is C 8∑_i=4^12a_i=∑_i=1^12a_i ∑_i=1^3a_i ⇒∑_i=4^12a_i = 122(2a_1+11d) 32(2a_1+2d) ⇒122(2a_1+11d) 32(2a_1+2d)=63 ⇒ 9a_1 + 63d=63 ⇒ a+7d=7 ⇒ ...

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Byju's Answer

Standard XII

Mathematics

Geometric Mean

Let a 1, a 2,...

Question

Let $a_{1}, a_{2}, a_{3}, \dots$ be an arithmetic progression with npn-zero common difference. It is given that $12 \sum i = 4 a_{i} = 63$ and $a_{k} = 7$ for some $k$ . Then the value of $k$ is

6

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Solution

The correct option is C $8$
$12 \sum i = 4 a_{i} = 12 \sum i = 1 a_{i} - 3 \sum i = 1 a_{i}$
$\Rightarrow 12 \sum i = 4 a_{i} = \frac{12}{2} (2 a_{1} + 11 d) - \frac{3}{2} (2 a_{1} + 2 d) \Rightarrow \frac{12}{2} (2 a_{1} + 11 d) - \frac{3}{2} (2 a_{1} + 2 d) = 63 \Rightarrow 9 a_{1} + 63 d = 63 \Rightarrow a + 7 d = 7 \Rightarrow a_{8} = 7$

Hence $k = 8$

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