The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary). 12,18,27. Find the 8th term

Answer 1

18 = 12·3/2; 27 = 18·(3/2) = 12(3/2)²; a₈ = 12(3/2)⁷ = 205.031

Answer 2

Make a difference table.

The 2nd differences appear to be constant and equal to 3.

Use the Newton forward formula: u_n=u₀+nΔu₀+(1/2)n(n-1)Δ²u₀ to get your answer or to set up the quadratic expression: u_n=(1/2)(3n²+9n+24).

This last expression assumes that u₀=12 (not u₁) so the 8th term maybe thought of as u₇ (i.e. n=7 in the formula).

Please note that this answer satisfies the problem with integer answers, but the terms are quite different from the answers given by assuming that this is a geometric sequence with common ratio of 3/2!

Answer 3

Hi George,

This is a geometric sequence. Formula for those is:

a_n = a₁ * r^n-1

n=number of the term you are looking for

a₁= First term

r= common ratio

Here:

n=8

a₁= 12

r= (18/12) = (27/18) = (3/2)

Plug these values into the formula above, and you should be able to compute a₈. I hope this helps.