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

Given that
$\begin{array}{l} a_{3} + a_{5} + a_{8} = 11 \\ \Rightarrow a + 2 d + a + 4 d + a + 7 d = 11 \\ or 3 a + 13 d = 11 . . . . . . . . . (1) \end{array}$
Given
$\begin{array}{l} a_{4} + a_{2} = - 2 \\ \Rightarrow a + 3 d + a + d = - 2 \\ or a = - 1 - 2 d . . . . . . . . . (2) \end{array}$
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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