First slide

Arithmetic progression

Question

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

Moderate

A

-8
B

5
C

7
D

9

Solution

$\begin{array}{l} Given that a_{3} + a_{5} + a_{8} = 11 \\ \Rightarrow a + 2 d + a + 4 d + a + 7 d = 11 \\ \Rightarrow 3 a + 13 d = 11 \\ Given a_{4} + a_{2} = - 2 \\ \Rightarrow a + 3 d + a + d = - 2 \\ \Rightarrow a = - 1 - 2 d \end{array}$
Putting value of ‘a’ from (2) in (1), we get
$\begin{array}{l} 3 (- 1 - 2 d) + 13 d = 11 \Rightarrow 7 d = 14 \Rightarrow d = 2 and a = - 5 \\ \Rightarrow a_{1} + a_{6} + a_{7} = 7 \end{array}$

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