Question

What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is
781,250?

Answer 1

\[[a_{1}, a_{2},a_{3},a_{4},a_{5},a_{6},a_{7},a_{8}]\], and \[a_1=10,\] and \[a_{8}=781,250\], with a geometric sequence there is a constant ratio, a value that each term is multiplied by to get the next term

Answer 2

So, \[a_{1} = 10, a_{2} = a_{1} * r, a_{3}=a_{1}*r^2 ... a_{8} = a_{1}*r^{7}\]

Answer 3

You need to find "r" based upon this fact that \[a_{8} = 781,250 = a_{1}*r^7\]

Answer 4

You have \[a_{1}\] and once you find "r" you can then easily find the sum of the geometric sequence

Answer 5

the sum of the serious would be \[\sum_{0}^{n}a*r^k = \frac{a(1-r^{n+1})}{1-r}\], here \[a_{1} = 10*r^{0}\], so "a" in the above equation would be 10

Answer 6

i can't figure out what r is

Answer 7

r=5