What is the sum of a 6–term geometric series if the first term is 21 and the last term is 1,240,029?

Question

anonymous · Answer

anyone? Please help me!

amistre64 · Answer

do you recall any formulas that might help out?

anonymous · Answer

a(1)-a(a)r^n/1-r
?

amistre64 · Answer

the formula for a sum of a geo progression requires us to find the first term, the number of terms, and the common ratio

thats the one

anonymous · Answer

how do you find the common ratio though?

amistre64 · Answer

and the formula for a general term of the a geo seq is?

amistre64 · Answer

an = a1 * r^n

(an/a1)^(1/n) = r

amistre64 · Answer

err, make that n-1

amistre64 · Answer

an = a1 * r^(n-1)

(an/a1)^(1/(n-1)) = r

better :)

anonymous · Answer

sorta. im still confused though. So wait I plug the numbers in and get 1,240,029/21^1/6-1

amistre64 · Answer

a1=21, a6=that big number, and n=6$$r=\left(\frac{big}{21}\right)^{1/6}$$

amistre64 · Answer

err, 1/5  yes

amistre64 · Answer

im only slightly confused lol

anonymous · Answer

haha Im lost. this stuff confuses me more than anything

amistre64 · Answer

so:

21(1-( 1240029/21)^6/5)/(1-(1240029/21))  is what i would type into the wolf for simplicity

anonymous · Answer

whats the wolf?

amistre64 · Answer

http://www.wolframalpha.com/input/?i=21%281-%28+1240029%2F21%29%5E%286%2F5%29%2F%281-%281240029%2F21%29%29

amistre64 · Answer

thisis the wolf, and i syntaxed it wrong, this ones better http://www.wolframalpha.com/input/?i=21%281-%28+1240029%2F21%29%5E%286%2F5%29%29%2F%281-%281240029%2F21%29%29

anonymous · Answer

ughh thankyou but thats not an answer choice :(
these are the choices
1,395,030

 1,461,460

 1,527,890

 1,594,320

amistre64 · Answer

lets chk my mathing then ....

anonymous · Answer

okay thankyou! I wish I understood this

amistre64 · Answer

need the "r" value; everything else is given

$$a_n=a_1*r^{n-1}$$
$$\frac{a_n}{a_1}=r^{n-1}$$
$$\left(\frac{a_n}{a_1}\right)^\frac{1}{n-1}=r$$
$$\left(\frac{a_6}{a_1}\right)^\frac{1}{5}=r=\left(\frac{1240029}{21}\right)^\frac{1}{5}$$

amistre64 · Answer

ohhh, i left off the 1/5 in the wolf lol

amistre64 · Answer

http://www.wolframalpha.com/input/?i=21%281-%28%281240029%2F21%29%5E%286%2F5%29%29%29%2F%281-%281240029%2F21%29%5E%281%2F5%29%29 139...

anonymous · Answer

oh my gosh! Thankyou so much! I get it now! See I didnt realize you had to use the same formula and solve for "r"! I thought it was a different formula that I didnt have! thanky so much!

amistre64 · Answer

good luck :)