Question
which of the followign correctly uses the explict formula An=1/4+(n+1)x1/2 to find the 9th termof the described arthermic sequence
Answers
GPT-4o mini
To find the 9th term of the arithmetic sequence using the explicit formula \( A_n = \frac{1}{4} + (n + 1) \cdot \frac{1}{2} \), we need to substitute \( n = 9 \) into the formula.
Let's calculate \( A_9 \):
\[
A_9 = \frac{1}{4} + (9 + 1) \cdot \frac{1}{2}
\]
\[
A_9 = \frac{1}{4} + 10 \cdot \frac{1}{2}
\]
\[
A_9 = \frac{1}{4} + 5
\]
To add these, we can convert 5 into a fraction with a denominator of 4:
\[
5 = \frac{20}{4}
\]
Now we can add \( \frac{1}{4} \) and \( \frac{20}{4} \):
\[
A_9 = \frac{1}{4} + \frac{20}{4} = \frac{21}{4}
\]
Thus, the 9th term of the arithmetic sequence is \( \frac{21}{4} \) or \( 5.25 \).
Let's calculate \( A_9 \):
\[
A_9 = \frac{1}{4} + (9 + 1) \cdot \frac{1}{2}
\]
\[
A_9 = \frac{1}{4} + 10 \cdot \frac{1}{2}
\]
\[
A_9 = \frac{1}{4} + 5
\]
To add these, we can convert 5 into a fraction with a denominator of 4:
\[
5 = \frac{20}{4}
\]
Now we can add \( \frac{1}{4} \) and \( \frac{20}{4} \):
\[
A_9 = \frac{1}{4} + \frac{20}{4} = \frac{21}{4}
\]
Thus, the 9th term of the arithmetic sequence is \( \frac{21}{4} \) or \( 5.25 \).