Posted by **Serina** on Wednesday, January 5, 2011 at 5:25am.

sum of 2nd and 5th terms of a geometric sequence is 13. the sum of the 3rd and 6th is -39.

determine:

a) the ratio "r" of the sequence

b) the first term "a" of the sequence

- Math 12 -
**drwls**, Wednesday, January 5, 2011 at 8:55am
The sequence is or the form

a(1 + r + r^2 + ...)

The first term is a1 = a

The second term is a2 =a*r

The nth term is an = a*r^*(n-1)

Here is what you know:

a*r + a*r^4 = 13

a*r^2 + a*r^5 = -39

These two equations require that

-39 = r*13. Therefore

r = -3

Now that you know r, solve the first equation for a:

a*(-3 + 81) = 13

78 a = 13

a = 1/6

The sequence is:

1/6, -1/2, 3/2, -9/2, 27/2, -81/2 ...

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