Question

In a certain sequence, each term, starting with the 3rd term, is found by multiplying the previous two terms. what is the difference between the 6th and 3rd terms in the sequence? (1) the 1st term is equal to 8 times the 2nd term. (2) the 4th term is equal to 1.

Answer 1

From F.S 1, consider this series : 8, 1, 8, 8, 64, 64*8. 

Again, consider the series 2, 1/4, 1/2, 1/8, 1/16, 1/(8*16). Clearly, the difference of the 6th and the 3rd term is different for them. Insufficient.

From F.S 2, let the series be a,b,ab,ab2,a2b3,a3b5a,b,ab,ab2,a2b3,a3b5. Now we know that ab2=1ab2=1. The required difference =a3b5−ab=ab(a2b4−1)=ab[(ab2)2−1]a3b5−ab=ab(a2b4−1)=ab[(ab2)2−1]= 0.Sufficient.