Friday

January 30, 2015

January 30, 2015

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

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 9:15pmYou 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

**Answer this Question**

**Related Questions**

math studies - An arithmetic series has a first term of -4 and a common ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

arithmetic - 1. The first and last term of an A.P are, a and l respectively, ...

Math - the sum of the first n terms of an arithmetic series is -51. the series ...

Advanced Functions - I need help answering these questions 1. State the Common ...

arithmetic - In an arithmetic series, the terms of the series are equally spread...

Maths - 1..The first 2 terms of a geometric progression are the same as the ...

Algebra - In an arithmetic series, the terms of the series are equally spread ...

math - The sum of the first 20 terms of an arithmetic series is identical to the...

arithmetic - The sum of the first 4 terms of an arithmetic series is -8 and the ...