the first three terms of an arithmethic series have a sum of 24 and a product of 312. What is the fourth term of the series?

3,8,13,?

You should be able to figure out the 4th term now

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how did u figure that out ?

The sum of an arithmetic series is given by:


Knowing that, you can get from your given information that:




Solving both equations simultaneously yields the answer. For the second part, simply find the common difference and add it to the third term.

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a + (a + d) + (a + 2d) = 24 => 3a + 3d = 24 => a + d = 8 => a = 8 - d .... (1)

a(a + d)(a + 2d) = 312 .... (2)

Substitute (1) into (2): (8 - d)(8)(8 + d) = 312 => (8 - d)(8 + d) = 39 => 64 - d^2 = 39 => d^2 = 25 => d = 5 or -5.

Case 1: d = 5 => a = 3.

Case 2: d = -5 => a = 13.

It's left for you to find the fourth term of the series in each case.

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1. There are two things you should never try to prove ...... the impossible and the obvious.

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3. Lack of planning on your part does not constitute an emergency on my part.

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