Problem : What is the common ratio r in the geometric sequence .5, 1.5, 4.5, 13.5, 40.5,…?

r = 3.

Problem : Define the geometric sequence an = 2×3(n - 1) recursively.

a1 = 2; an+1 = 3an.

Problem : Define the geometric sequence a1 = 4; an+1 = an explicitly.

an = 4×(n - 1)

Problem : What is 53×2(n - 1)?

S15 = a1( = 3() = 3() = 98301.

Problem : What is the limit of the infinite series 2 + 1 + + + ... ?

a1rn-1 = = = 4.