If un = 2, 6, 10, ..., the last tem of the sequence is 90. The number of terms in the sequence is
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Correct Answer: Option D
Explanation:
To determine the number of terms in the arithmetic sequence where the first term \( u_1 = 2 \), the common difference \( d = 4 \) (since \(6 - 2 = 4\)), and the last term \( u_n = 90 \), we can use the formula for the \( n \)-th term of an arithmetic sequence:
\[
u_n = u_1 + (n - 1) \times d
\]
Step-by-Step Calculation:
1. Plug in the values:
\[
90 = 2 + (n - 1) \times 4
\]
2. Simplify the equation:
\[
90 - 2 = (n - 1) \times 4
\]
\[
88 = (n - 1) \times 4
\]
3. Solve for \( n \):
\[
n - 1 = \frac{88}{4} = 22
\]
\[
n = 22 + 1 = 23
\]
The number of terms in the sequence is 23.
The correct answer is D. 23
To determine the number of terms in the arithmetic sequence where the first term \( u_1 = 2 \), the common difference \( d = 4 \) (since \(6 - 2 = 4\)), and the last term \( u_n = 90 \), we can use the formula for the \( n \)-th term of an arithmetic sequence:
\[
u_n = u_1 + (n - 1) \times d
\]
Step-by-Step Calculation:
1. Plug in the values:
\[
90 = 2 + (n - 1) \times 4
\]
2. Simplify the equation:
\[
90 - 2 = (n - 1) \times 4
\]
\[
88 = (n - 1) \times 4
\]
3. Solve for \( n \):
\[
n - 1 = \frac{88}{4} = 22
\]
\[
n = 22 + 1 = 23
\]
The number of terms in the sequence is 23.
The correct answer is D. 23