Question

Write an explicit formula for a(n), the n^th term of the sequence 8, 48, 288,...

Answer 1

Answer:

a(n) = 8 x 6^(n-1)

Explanation:

The sequence 8, 48, 288, ... is geometric because each term is the term before multiply by a common ratio, so:

8

8 x 6 = 48

48 x 6 = 288

Therefore, the equation of a geometric sequence is:

$a_n=a_1r^{n-1}$

Where a1 is the first term of the sequence and r is the common ratio. So, replacing a1 by 8 and r by 6, we get that the equation fo the n^th term of the sequence is:

$a_n=8\cdot6^{n-1}$

So, the answer is:

a(n) = 8 x 6^(n-1)