# College Algebra Questions:?

Hello All-

I have two College Algebra Questions that i need help with.

1- Find the sum, if it exists. 7 + 2 + 4/7 +8/49 + ........

2- Find the sum of the first 7 terms in the geometric series: 3 + 9 + 27 + .......

Thanks so much for the help in advance.

Relevance
• The sum of an infinite geometric series = a/(1-r) where 'a' is your first term and 'r' is the ratio of successiver terms. For problem #1, a=7 and r=2nd term/1st term=2/7. The sum would then be:

S = 7/(1-2/7) = 7/(5/7) = 49/5 = 9.8

A finite geometric series has a sum = a(1-r^n)/(1-r), where 'a' and 'r' are the same as before, and 'n' is the number of terms. The sum in this case is:

3(1-3^7)/(1-3) = 3(-2186)/(-2) = 3279

• 2. 3+9+27+81+243+729+2187=3279

• ok, so (4x + 5)^3 = (4x + 5)*(4x + 5)*(4x + 5). utilising the FOIL technique (first, outdoors, interior, final), you may boost (4x + 5)*(4x + 5) to 16x^2 + 40x + 25. Then, you may desire to multiply this finished expression by utilising 4x + 5, which will seem complicated, even with the undeniable fact that this is incredibly no longer. (4x + 5) * (16x^2 + 40x + 25) = 64x^3 + 80x^2 + 160x^2 + 200x + 100x + a hundred twenty five. This simplifies to 64x^3 + 240x^2 + 300x + a hundred twenty five. it relatively is the accelerated answer. i'm hoping this facilitates!

• 1. 9 36/49

2. 3279