Two Terms of Geometric Sequence Find the explicit rule

Question

Two terms of a geometric sequence are a_4=54 and a_9=13,122. Write an explicit rule for the nth term.

a_n=

Answer 1

Geometric, not arithmetic.

can derive using a9/a4 = r^5. solve for r. Then, a4 = cr^4. Solve for c.

Number sense way 100 < a9/a4 < 1000. Only one integer has 100 < r^5 < 1000, 3

54 = c*3^4 = 81c

c = 2/3

an=2/3*3^n or 2 * 3^(n-1)

Check for a9

2*3^(9-1) = 2*3^8 = 13122

Yep, that's the solution.

Answer 2

a_n = a_1 + (n-1)r

a_9 = 54 + (9-4)(2613.6) = 54+5(2613.6) = 54 + 13068 = 13,122

a_n = a_1 +(n-1)(2613.6)