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

• A. 5,120
• B. 1,280
• C. 10,240
• D. 2,560

Answer: (D)

Verified step by step guidance

1. Identify the formula for the nth term of a geometric sequence, which is given by: $a{n}_{\mathrm{th}}=a{1}_{}{r}^n-1$.
2. Substitute the given values into the formula: $a{\mathrm{10}}_{}=52^{(}$.
3. Simplify the exponent: $2^{(}$ becomes $2^9$.
4. Calculate the power of 2: $2^9$.
5. Multiply the result by the first term: $52^9$ to find the 10th term.