Posted by **Estrick Abel** on Saturday, March 23, 2013 at 7:38pm.

1)The sum of 6 terms of an arithmetic series is 45, the sum of 12 terms is -8. Find the first term and the common difference?

2)If in a geometric sequence the sum of the second and the third is 20 and the sum of the fourth and fifth is 320, find the common ratio and the first term. Assume that the common ratio is possitive.

- Math(arithmetic & Geometric Series) -
**Reiny**, Saturday, March 23, 2013 at 9:15pm
You have to know the formula for the sum of n terms of an AS

Sum(6) = 3(2a + 5d)

6a + 15d = 45 --- #1

sum(12) = 6(2a + 11d ) = -8

12a + 66d = -8

6a + 33d = -4 ---#2

subtract them

18d = -49

d = -49/18

back in #1

6a + 15(-49/18) = 45

6a = 45 + 735/18

6a = 515/18

a = 515/36

expected nicer numbers....

#2:

ar + ar^2 = 20 ---> ar(1 + r) = 20 ----#1

ar^3 + ar^4 = 320 ---> ar^3(1 + r) = 320 ---#2

divide #2 by #1

r^2 = 16

r = 4 , you said r is positive

in #1

4a(5) = 20

a = 1

a = 1 , r = 4

check:

terms would be

1 4 16 64 256

and 4+16 = 20

and 64 + 256 = 320

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