First slide

Arithmetic progression

Question

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

NA

Solution

$a + 2 d + a + 4 d + a + 7 d = 11 \Rightarrow 3 a + 13 d = 11 \to (1)$
$\begin{array}{l} \Rightarrow a + 3 d + a + d = - 2 \Rightarrow a + 2 d = - 1 \to (2) \\ From (1) and (2) \Rightarrow d = 2, a = - 5 \end{array}$
$∴ a_{1} + a_{6} + a_{7} = 3 a + 11 d = 7$

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