Question

A sequence has an initial value of 10 and each term is twice the previous.  Which function models this sequence?

1. a(n)=10(2)"n
2. a(n)=10(2)n-1
3. a(n)=10+2n
4. a(n)=10+2(n-1)

Answer 1

`10,\ 20,\ 40,\ 80,\ ...\\\\a_n=2\cdot a_(n-1)\ \ \ \Rightarrow\ \ \ q=2\\\\geometric\ sequence \ \ \ \Rightarrow\ \ \ a_n=a_1\cdot q^(n-1)\\\\a_1=10\ \ \ and\ \ \ q=2 \ \ \ \Rightarrow\ \ \ a_n=10\cdot 2^(n-1)\\\\Ans.\ this\ sequence\ models:\ \ \ a_n=10\cdot 2^(n-1)`