Question

Sum and product of three consecutive terms of an AP are 15 and 80 respectively . Find the terms​

Answer 1

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

Let a and d be the first term and common difference of the A.P respectively

Consider a,a + d and a - d to be the three terms

According to the Question,

a + (a + d) + (a - d) = 15

» 3a = 15

» a = 5

Also,

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

»5(5 + d)(5 - d) = 80

» 25 - d² = 16

» d² = 9

» d = ± 3

When d = 3,

The terms would be:

5,8,11,.............

When d = -3,

The terms would be:

5,2, -1,.............

Answer 2

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Let first term be a.

Common difference be d.

And let three consecutive terms be a , a + d and a - d

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A.T.Q,

Sum of terms = 15

a + (a + d) + (a - d) = 15

a + a + d + a - d = 15

3a = 15

a = 15/3

$\LARGE{\implies}{\boxed{\boxed{\sf{a \: = \: 5}}}}$

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Now products

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

________[Put value of a]

5(5 - d)(5 + d) = 80

(25 - 5d)(5 + d) = 80

125 + 25d - 25d - 5d² = 80

125 - 5d² = 80

-5d² = 80 - 125

-5d² = -45

5d² = 45

d² = 45/5

d² = 9

d = √9

$\LARGE{\implies}{\boxed{\boxed{\sf{d \: = \: ± \: 3 }}}}$

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So, terms are

1) d = +3

5,8,11

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2) d = -3

5,2,-1