SOLUTION: The first three terms of a G.P are x+1, x+3 and x+8, find, i) The Value of x ii) The common ratio iii) The sum of the first 15 terms.

Question 1127671: The first three terms of a G.P are x+1, x+3 and x+8, find,
i) The Value of x
ii) The common ratio
iii) The sum of the first 15 terms.
Found 4 solutions by FrankM, htmentor, MathLover1, MathTherapy:
Answer by FrankM(1040)   (Show Source): You can put this solution on YOUR website!
For there to be a common ratio,

And after cross multiplying -
X^2+9X+8= X^2+6X+9

9X+8=6X+9
3X=1
i) X= 1/3
ii) Therefore the first 3 numbers are 4/3, 10/3, 25/3 with a common ratio of 2.5
iii) = A (1+r^n)/(1-r) = 4/3 (1-2.5^15)/(1-2.5)

4/3 (-931321.575)/-1.5 = 827841.4

.

I used a spreadsheet to verify the solution is correct.

Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
The common ratio r = (x+3)/(x+1) = (x+8)/(x+3)
Solve for x:
x^2 + 6x + 9 = x^2 + 9x + 8
3x = 1
x = 1/3
Therefore r = (1/3 + 3)/(1/3 + 1) = 10/4
The sum of the first n terms of a G.P. = Sn = a1*(1-r^n)/(1-r)
S15 = (4/3)(1-(10/4)^15/(1-(10/4)) = 827841.4
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

the general form of a geometric progression(GP) is
with = first term, is the common ratio
we have , then

solve for

solve for

then,
i) The Value of

cross multiply the fractions

then
ii) The common ratio

iii) The sum of the first 15 terms.

the general form of a geometric progression(GP) is

the first 15 terms

the sum is:
≈

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The first three terms of a G.P are x+1, x+3 and x+8, find,
i) The Value of x
ii) The common ratio
iii) The sum of the first 15 terms.

I wonder if the person who calculated EACH term and then added all 15 would do the same if the question asked for the SUM of the first
100, 150, or 200 terms? If not, then why WOULD SHE do that here! RIDICULOUS!!!
Maybe she would have done the same thing, who knows!!
Why does this person continue to make these problems look so difficult and come up with the longest and most tedious way to solve these simple,
simple math problems?
BTW: The ratio is derived from the following, and by finding the value of x, first:
After x is found, substitute it into any of the 2 fractions to get the ratio.
Now, with the common ratio, or r, and the VALUE of the 1st term, we can determine the sum of any number of consecutive terms by using the following formula:
You should get the same answer all 3 respondents came up with.
RELATED QUESTIONS
a). In an AP, the first term -5 and the last term is 105. If the sum of these terms is... (answered by ikleyn)
The first three terms of a geometric progression are x+1, x-3 and x-1. Find (i) the... (answered by josgarithmetic)
The first three terms of geometric progression are x+1, x-3 and x-1. find i) the value... (answered by rothauserc)
Given that x+6,x and x-3 are the first three terms of geometric progression.calculate the (answered by htmentor)
The first three consecutive terms of an exponential sequence are (x-1), 2x and (5x+3)... (answered by greenestamps)
the first numbers p-1,2p-2 and 3p-1 are the first three terms of a Go where p>0 find... (answered by htmentor)
The three consecutive terms of exponential sequence are x-1,2x&5x+3,find(1)x(2) find... (answered by greenestamps)
The three consecutive terms of exponential sequence are x_1,2x,&5x+3,find (1)x(2) find... (answered by ikleyn)
the sum of first two terms of a G P is x and the sum of last two terms is y. if there are (answered by rothauserc)