Questions: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of the sequence with the given first term, a1, and common ratio, r. Find a12 when a1=2, r=2. A) 8192 B) 4100 C) 4096 D) 24

Solution Steps

The formula for the nth term of a geometric sequence is given by:

\[ a_n = a_1 \cdot r^{n-1} \]

where \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.

We are given \(a_1 = 2\), \(r = 2\), and we need to find \(a_{12}\). Substitute these values into the formula:

\[ a_{12} = 2 \cdot 2^{12-1} = 2 \cdot 2^{11} \]

Calculate \(2^{11}\):

\[ 2^{11} = 2048 \]

Now, substitute \(2^{11} = 2048\) back into the equation:

\[ a_{12} = 2 \cdot 2048 = 4096 \]

Final Answer