For an increasing A-P- a1- a2- a3- anif a1-a3-a5-12 and a1- a3- a5-80- then which of the following is true-A- a 2-1B- a1-2C- a 3-4D- a5-2

The correct option is D a_5 = + 2 a_1 + a_3 + a_5 = 12 a + a + 2d + a + 4d = 12 a + 2d = 4 a_1 · a_3· a_5 = 80 a(a + 2d) (a+4d)=80 (a) ( 4)(a+4d) = 80 a(a ...

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Byju's Answer

Standard XII

Mathematics

Sum of n Terms

For an increa...

Question

For an increasing A.P. $a_{1}, a_{2}, a_{3} . . . a_{n}$ ,
if $a_{1} + a_{3} + a_{5} = - 12$ and $a_{1} \cdot a_{3} \cdot a_{5} = 80$ , then which of the following is true.

$a_{1} = + 2$

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$a_{2} = - 1$

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$a_{3} = 4$

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$a_{5} = + 2$

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Solution

The correct option is D
$a_{5} = + 2$

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

$a + a + 2 d + a + 4 d = - 12$

$a + 2 d = - 4$

$a_{1} \cdot a_{3} \cdot a_{5} = 80$

$a (a + 2 d) (a + 4 d) = 80$

$(a) (- 4) (a + 4 d) = 80$

$a (a + 4 d) = - 20$

$(- 4 - 2 d) (- 4 + 2 d) = - 20$

$4 d^{2} - 16 = 20$

$d = \pm 3 \Rightarrow d = + 3$

Hence $a = - 10$

So, $a_{5} = 2$

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Similar questions

Q. For an increasing A.P.

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

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

and

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, then which of the following is (are) TRUE?

Q. If

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

then

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

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

and

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

then the value of

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

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

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and

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

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

equals

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a_{1}, a_{2}, a_{3}, . . . . ., a_{n}, . . . ., a_{1} + a_{3} + a_{5} = - 12

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For an increasing A.P. a1,a2,a3...an, if a1+a3+a5=−12 and a1⋅a3⋅a5=80, then which of the following is true.

The correct option is D a5=+2 a1+a3+a5=−12 a+a+2d+a+4d=−12 a+2d=−4 a1⋅a3⋅a5=80 a(a+2d)(a+4d)=80 (a)(−4)(a+4d)=80 a(a+4d)=−20 (−4−2d)(−4+2d)=−20 4d2−16=20 d=±3⇒d=+3 Hence a=−10 So, a5=2

For an increasing A.P. $a_{1}, a_{2}, a_{3} . . . a_{n}$ ,
if $a_{1} + a_{3} + a_{5} = - 12$ and $a_{1} \cdot a_{3} \cdot a_{5} = 80$ , then which of the following is true.