How do you write an nth term rule for a_3=10a3=10 and a_6=300a6=300?

1 Answer
Feb 23, 2018

a_n=1.0359*3.107^(n-1)an=1.03593.107n1

Explanation:

I'm assuming this is a geometric sequence...

The general formula for an arithmetic sequence is

a_n=a_1*r^(n-1)an=a1rn1 with a_1a1 as the first term and rr as the common ratio.

Plug in:

a_3=10=a_1*r^(3-1)a3=10=a1r31
a_6=300=a_1*r^(6-1)a6=300=a1r61

10=a_1*r^(2)10=a1r2
300=a_1*r^(5)300=a1r5

Divide:

300/10=(a_1*r^(5))/(a_1*r^(2))30010=a1r5a1r2

30=(cancel(a_1)*r^(5))/(cancel(a_1)*r^(2))

30=r^3

root3(30)=r or 30^(1/3)

r~~3.107

Then find a_1:

10=a_1*9.653

a_1~~1.0359

Plug in the information into the general formula:

a_n=1.0359*3.107^(n-1)

Note: This is not exact as I rounded somewhere.