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nth Term of A.P

Let a1,a2,a3,...

Question

Let $a_{1}, a_{2}, a_{3}, \dots$ be an A.P. 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

A

- 8

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B

5

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C

7

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D

9

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Solution

The correct option is C $7$
Let $a$ be the first term and $d$ be the common difference of A.P.
Given that
$a_{3} + a_{5} + a_{8} = 11 \Rightarrow a + 2 d + a + 4 d + a + 7 d = 11 \Rightarrow 3 a + 13 d = 11 \dots (1)$

and $a_{4} + a_{2} = - 2$
$\Rightarrow a + 3 d + a + d = - 2 \Rightarrow 2 a + 4 d = - 2 \Rightarrow a = - 1 - 2 d \dots (2)$
Putting values of $a$ from eq $(2)$ in eq $(1)$ , we get
$3 (- 1 - 2 d) + 13 d = 11 \Rightarrow 7 d = 14 \Rightarrow d = 2$
$∴ a = - 5$
Hence, $a_{1} + a_{6} + a_{7} = 3 a + 11 d = 7$

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Similar questions

a_{1}, a_{2}, a_{3}, \dots

be an A.P. such that

a_{3} + a_{5} + a_{8} = 11

a_{4} + a_{2} = - 2

. Then the value of

a_{1} + a_{6} + a_{7}

Q. For an A.P.,

a_{1}, a_{2}, a_{3}, \dots \dots

a_{3} + a_{5} + a_{8} = 11

a_{4} + a_{2} = - 2

, then the value of

a_{1} + a_{6} + a_{7}

A . P .

a_{1}, a_{2}, a_{3}, . . . . . ., a_{n}, . . . . .

a_{1} + a_{3} + a_{5} = - 12

a_{1} a_{2} a_{3} = 8

then the value of

a_{2} + a_{4} + a_{6}

Q. If for an A.P.

a_{1}, a_{2}, a_{3} . . . . . . . . . a_{n},

a_{1} + a_{3} + a_{5} = - 12

a_{1} a_{2} a_{3} = 8

then the value of

a_{2} + a_{4} + a_{6}

{(1 + x)}^{10} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . . . a_{10} x^{10}

, then value of

{(a_{0} - a_{2} + a_{4} - a_{6} + a_{8} - a_{10})}^{2} + {(a_{1} - a_{3} + a_{5} - a_{7} + a_{9})}^{2}

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nth Term of A.P

Standard XIII Mathematics

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