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The sum of three consecutive terms in an A.P. is 6 and their p

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The sum of three consecutive terms in an A.P. is $6$ and their product is $- 120$ . Find the three numbers.

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The sum of three consecutive terms in an A.P. is

6

and their product is

- 120

. Find the three numbers.

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Let

a - d, a, a + d

be the first three terms of an A.P.

It is given that the sum of the terms is

6

that is:

a - d + a + a + d = 6 \Rightarrow 3 a = 6 \Rightarrow a = \frac{6}{3} \Rightarrow a = 2...... (1)

It is also given that the product of the terms is

- 120

that is:

(a - d) (a) (a + d) = - 120 \Rightarrow a (a^{2} - d^{2}) = - 120 (∵ (x + y) (x - y) = x^{2} - y^{2}) \Rightarrow 2 (2^{2} - d^{2}) = - 120 (F ro m (1)) \Rightarrow 4 - d^{2} = - \frac{120}{2}

\Rightarrow 4 - d^{2} = - 60 \Rightarrow d^{2} = 4 + 60 \Rightarrow d^{2} = 64 \Rightarrow d = \pm 64 \Rightarrow d = \pm 8........... (2)

Now, if

a = 2

and

d = - 8

then the first three terms of the A.P are:

a - d = 2 - (- 8) = 2 + 8 = 10

a = 2

and

a + d = 2 - 8 = - 6

And if

a = 2

and

d = 8

then the first three terms of the A.P are:

a - d = 2 - 8 = - 6

a = 2

and

a + d = 2 + 8 = 10

Hence, the three terms are

- 6, 2, 10

10, 2, - 6

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Question Text	The sum of three consecutive terms in an A.P. is $6$ and their product is $- 120$ . Find the three numbers.
Answer Type	Text solution:1
Upvotes	150

The sum of three consecutive terms in an A.P. is 6 and their product is −120. Find the three numbers.

Text solutionVerified

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The sum of three consecutive terms in an A.P. is $6$ and their product is $- 120$ . Find the three numbers.