Problem

Consider the sequence: 3, 6, 12, 24, 48, ___. What is the next term of the sequence?

Answer

Expert–verified
Hide Steps
Answer

Substitute the values into the formula: \(a_n = 3 \times 2^{(6-1)}\)

Steps

Step 1 ：The given sequence is a geometric sequence where each term is twice the previous term.

Step 2 ：The rule for the nth term of a geometric sequence is given by \(a_n = a_1 \times r^{(n-1)}\), where \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.

Step 3 ：In this sequence, \(a_1 = 3\) and \(r = 2\). We are looking for the 6th term, so \(n = 6\).

Step 4 ：Substitute the values into the formula: \(a_n = 3 \times 2^{(6-1)}\)

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More