If an and cn equal the following find the product of the sum

If {a_n} and {c_n} equal the following find the product of the sum of the first 6 terms of {a_n} and the sum of the infinite series containing all the terms of {c_n}. {a_n} = -4, 16, -64, 256, ... {c_n} = -9, 1, -1/9, 1/81, ... What is the sum, S_6, of the first 6 terms of {a_n}? S_6 =

Solution

a₆=(-4)(-4⁶-1)/(-4-1)=3276

c_n=a/(1-r)=(-9)/(1-(-1/9)=-81/10

a₆*c_n=-26535.6

And that\'s the answer