jmc

Question

An infinite geometric series has a first term of 12 and a second term of 4. A second infinite geometric series has the same first term of 12, a second term of 4+n, and a sum of four times that of the first series. Find the value of n.

Accepted Answer

Note that if the the two series have constant ratios of a and b, respectively, then 4( 121-a ) = 121-b. Simplifying, 4(1-b)=1-a. Substituting in a= 412=13 and b= 4+n12=13+n12, we quickly find that n=6.