For an A-P- a 1- a 2- a 3- - - if a 3- a 5- a 8-11 and a 4- a 2-2- then the value of a 1- a 6- a 7 isA- 17B- 13C- 3D- 7

The correct option is D 7Let first term =a and common difference =d a_3+a_5+a_8=11 ⇒(a+2d)+(a+4d)+(a+7d)=11 ⇒ 3a+13d=11 ⋯(1) a_4+a_2= 2 ⇒ (a+3d)+(a+d)= 2 ...

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Byju's Answer

Standard XII

Mathematics

nth Term of A.P

For an A.P., ...

Question

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

17

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Solution

The correct option is D $7$
Let first term $= a$ and common difference $= d$
$a_{3} + a_{5} + a_{8} = 11$
$\Rightarrow (a + 2 d) + (a + 4 d) + (a + 7 d) = 11$
$\Rightarrow 3 a + 13 d = 11 \dots (1)$

$a_{4} + a_{2} = - 2$
$\Rightarrow (a + 3 d) + (a + d) = - 2$
$\Rightarrow a + 2 d = - 1 \dots (2)$

Solving equation $(1)$ and $(2)$ , we get
$a = - 5, d = 2$
Now, $a_{1} + a_{6} + a_{7}$
$= 3 a + 11 d$
$= - 15 + 22 = 7$

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Similar questions

Q. Let

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

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

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

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then the value of

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For an A.P., a1, a2, a3,……, if a3+a5+a8=11 and a4+a2=−2, then the value of a1+a6+a7 is

The correct option is D 7Let first term =a and common difference =d a3+a5+a8=11 ⇒(a+2d)+(a+4d)+(a+7d)=11 ⇒ 3a+13d=11 ⋯(1) a4+a2=−2 ⇒ (a+3d)+(a+d)=−2 ⇒ a+2d=−1 ⋯(2) Solving equation (1) and (2), we get a=−5 , d=2 Now, a1+a6+a7 =3a+11d =−15+22=7

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