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

Question

anonymous · Answer

$$[a_{1}, a_{2},a_{3},a_{4},a_{5},a_{6},a_{7},a_{8}]$$, 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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

i can't figure out what r is

anonymous · Answer

r=5