Find the $10^{\th}$ term of the geometric sequence in which $a_1=5$ and $r=2$.

• A. 5120
• B. 1280
• C. 10240
• D. 2560

Answer: (D)

Verified step by step guidance

1. Identify the formula for the nth term of a geometric sequence, which is given by: \( a_n = a_1 \cdot r^{(n-1)} \).
2. Substitute the given values into the formula: \( a_1 = 5 \), \( r = 2 \), and \( n = 10 \).
3. Calculate the exponent part of the formula: \( r^{(n-1)} = 2^{(10-1)} = 2^9 \).
4. Multiply the first term by the result of the exponentiation: \( a_{10} = 5 \cdot 2^9 \).
5. Simplify the expression to find the 10th term of the sequence.