1. ## arithmethic sequences help...

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?

2. 3,8,13,?

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

3. how did u figure that out ?

4. The sum of an arithmetic series is given by:
$\displaystyle S_n = n\left(\frac{t_1+t_n}{2}\right)$

Knowing that, you can get from your given information that:
$\displaystyle t_1 + t_2 + t_3 = 24$

$\displaystyle 24 = 3\left(\frac{t_1+t_3}{2}\right)$

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

5. Originally Posted by gendut3
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?
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.