25th term of the arithmetic sequence if a sub 1 is 1/2 and the common difference is -3/8

To find the 25th term of an arithmetic sequence, we can use the formula for the \( n \)-th term of an arithmetic sequence:

\[
a_n = a_1 + (n-1) \times d
\]

where:
- \( a_n \) is the \( n \)-th term of the sequence,
- \( a_1 \) is the first term of the sequence,
- \( d \) is the common difference, and
- \( n \) is the term number.

Given:
- \( a_1 = \frac{1}{2} \),
- \( d = -\frac{3}{8} \),
- \( n = 25 \).

Let's substitute the values into the formula:

\[
a_{25} = \frac{1}{2} + (25 - 1) \times \left(-\frac{3}{8}\right)
\]

Simplifying:

\[
a_{25} = \frac{1}{2} + 24 \times \left(-\frac{3}{8}\right)
\]

\[
a_{25} = \frac{1}{2} + \left(-\frac{72}{8}\right)
\]

\[
a_{25} = \frac{1}{2} - 9
\]

\[
a_{25} = \frac{1}{2} - \frac{18}{2}
\]

\[
a_{25} = \frac{1 - 18}{2} = \frac{-17}{2} = -8.5
\]

So, the 25th term of the arithmetic sequence is \( -8.5 \).

Would you like further details or have any questions?

Here are five related questions for further practice:
1. What is the 50th term of the same sequence?
2. How many terms of this sequence are greater than zero?
3. What is the sum of the first 25 terms of this sequence?
4. If the common difference were positive, how would it affect the 25th term?
5. What would be the 25th term if the first term were \( \frac{3}{4} \) instead?

**Tip:** When working with arithmetic sequences, always double-check the sign of the common difference as it significantly affects the sequence's behavior.

Learn how to find the 25th term of an arithmetic sequence using the formula for the nth term. This problem involves arithmetic sequences with a specific first term and common difference. Suitable for high school students studying sequences and series.

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