The Sum Of A Geometric Sequence Fomula Proof (S=a(1-r^n)/(1-r))

In this video you will be shown how to prove the formula for the sum of a geometric sequence. To do this first write out the sun as S=a+ar+ar^2+ar^(n-1). S stands for the sum of the geometric sequence, a is the first term of the geometric sequence, and n is the number of terms.

Next multiply this formula by r to give Sr=ar+ar^2+ar^3…+ar^n. Now subtract the second formula from the first formula to give S-Sr=a-ar^n (most of the middle terms will get cancelled out). Next factorise the left and right hand sides to give S(1-r)=a(1-r^n). Finally make S the subject by dividing by (1-r) which gives S=a(1-r^n)/(1-r).