Question 453276
the sum of the first n terms of a geometric series is given by the formula

{{{S[n] = a[1]*((1-r^n)/(1-r))}}}, 

where {{{a[1]}}} = the first term of the series, and r = common ratio.

1.  {{{a[1] = 256}}}, r = 3/4.

==> {{{S[7] = 256*((1-(3/4)^7)/(1-3/4))

= 14197/16 = 887.3125

}}}

2.   {{{a[1] = 1}}}, r = -3.

{{{S[10] = 1*((1-(-3)^10)/(1-(-3))) = -14762}}}


3. This is an arithmetic series, so  {{{S[n] = a[1] + (n-1)d = -14 + 9*7 = -14 + 63 = 49}}}.