If Un = 2, 6, 10...., the last term of the sequence is 90. The number of terms in the sequence is
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Correct Answer: Option D
Explanation:
To find the number of terms in the arithmetic sequence where the first term \( U_1 = 2 \), the common difference \( d = 4 \), and the last term is \( U_n = 90 \), use the formula for the \( n \)-th term of an arithmetic sequence:
\[
U_n = U_1 + (n - 1) \times d
\]
Step-by-Step Solution:
1. Substitute the given values into the formula:
\[
90 = 2 + (n - 1) \times 4
\]
2. Solve for \( n \):
\[
90 - 2 = (n - 1) \times 4
\]
\[
88 = (n - 1) \times 4
\]
\[
n - 1 = \frac{88}{4} = 22
\]
\[
n = 22 + 1 = 23
\]
The number of terms in the sequence is 23.
The correct answer is D. 23.
To find the number of terms in the arithmetic sequence where the first term \( U_1 = 2 \), the common difference \( d = 4 \), and the last term is \( U_n = 90 \), use the formula for the \( n \)-th term of an arithmetic sequence:
\[
U_n = U_1 + (n - 1) \times d
\]
Step-by-Step Solution:
1. Substitute the given values into the formula:
\[
90 = 2 + (n - 1) \times 4
\]
2. Solve for \( n \):
\[
90 - 2 = (n - 1) \times 4
\]
\[
88 = (n - 1) \times 4
\]
\[
n - 1 = \frac{88}{4} = 22
\]
\[
n = 22 + 1 = 23
\]
The number of terms in the sequence is 23.
The correct answer is D. 23.