First slide

Arithmetic progression

Question

$Consider an A.P, a_{1}, a_{2}, a_{3} \dots such that a_{3} + a_{5} + a_{8} = 11, and a_{4} + a_{2} = - 2 then the$ $value of a_{1} + a_{6} + a_{7} is$

Moderate

A

-8
B

5
C

7
D

9

Solution

$a_{3} + a_{5} + a_{8} = 11 \to 3 a + 13 d = 11 - - - (1) (n' t h t e r m i n A . P = a + (n - 1) d)$
$a_{4} + a_{2} = - 2 \Rightarrow 2 a + 4 d = - 2$
$\begin{array}{l} a = - 1 - 2 d - - - (2) \\ (1) and (2) \Rightarrow d = 2, a = - 5 \\ ∴ a_{1} + a_{6} + a_{7} = 3 a + 11 d = 7 \end{array}$

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