What is the 28th term of the sequence
an = an−1 + 5.2, if the 26th term is 42.3?

We are given the recursive formula for the sequence: 

\[
a_n = a_{n-1} + 5.2
\]

and the 26th term \( a_{26} = 42.3 \). To find the 28th term, we will use the recursive relation to calculate the terms leading to \( a_{28} \).

### Step-by-step solution:

1. **Find the 27th term:**

   \[
   a_{27} = a_{26} + 5.2 = 42.3 + 5.2 = 47.5
   \]

2. **Find the 28th term:**

   \[
   a_{28} = a_{27} + 5.2 = 47.5 + 5.2 = 52.7
   \]

Thus, the 28th term of the sequence is \( \boxed{52.7} \).

Would you like more details or further clarifications?

Here are some related questions to expand on this concept:

1. How would you generalize the formula for any \(n\)-th term if you know one specific term?
2. What would the 30th term of the sequence be, using the same formula?
3. If the difference between terms were \(6.8\) instead of \(5.2\), what would the 28th term be?
4. Can you express this sequence in a non-recursive (explicit) form?
5. How would the sequence change if \( a_{26} = 42.3 \) but the difference between terms was negative?

**Tip:** Always pay attention to whether a sequence is arithmetic or geometric when applying recursive relations.

What is the 28th term of the sequence an = an−1 + 5.2, if the 26th term is 42.3?

Learn how to find the 28th term of a recursive arithmetic sequence using the formula a_n = a_{n-1} + 5.2, given that the 26th term is 42.3. This step-by-step solution explains the process and concepts behind arithmetic sequences. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation