Question

What is the fourth term of the sequence below?

Please show your work and explain it!

a1 = 100, a_n = 0.4_a_n-1

Answer 1

What they are saying is the first term is 100 and to get each new term you should multiply the current term by .4. This is a recursive formula for a geometric sequence.

100, 100*.4, 100*.4*.4, etc.

The explicit form would be \[a _{n}=100(.4)^{n-1}\] where n is the term you are looking for.