Find the 10th term in each of the following A.P. a.5,7,9,11... b.5,8,11,14... c.24,21,18,15... d.-1,3,7,11...

To find the 10th term of an arithmetic progression (A.P.), we can use the formula for the \(n\)th term of an A.P.:

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

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

Let's find the 10th term (\(a_{10}\)) for each of the given A.P.s:

### a. A.P. 5, 7, 9, 11, ...
- First term (\(a_1\)) = 5
- Common difference (\(d\)) = 7 - 5 = 2

Using the formula:

\[
a_{10} = 5 + (10-1) \cdot 2 = 5 + 9 \cdot 2 = 5 + 18 = 23
\]

### b. A.P. 5, 8, 11, 14, ...
- First term (\(a_1\)) = 5
- Common difference (\(d\)) = 8 - 5 = 3

Using the formula:

\[
a_{10} = 5 + (10-1) \cdot 3 = 5 + 9 \cdot 3 = 5 + 27 = 32
\]

### c. A.P. 24, 21, 18, 15, ...
- First term (\(a_1\)) = 24
- Common difference (\(d\)) = 21 - 24 = -3

Using the formula:

\[
a_{10} = 24 + (10-1) \cdot (-3) = 24 + 9 \cdot (-3) = 24 - 27 = -3
\]

### d. A.P. -1, 3, 7, 11, ...
- First term (\(a_1\)) = -1
- Common difference (\(d\)) = 3 - (-1) = 3 + 1 = 4

Using the formula:

\[
a_{10} = -1 + (10-1) \cdot 4 = -1 + 9 \cdot 4 = -1 + 36 = 35
\]

### Summary of the 10th Terms:
- a. \(23\)
- b. \(32\)
- c. \(-3\)
- d. \(35\)

Would you like any further details or have any questions?

Here are 8 related questions you might consider:
1. How do you find the common difference in an A.P.?
2. What is the formula for the sum of the first \(n\) terms of an A.P.?
3. Can you derive the formula for the nth term of an A.P.?
4. How would you find the 15th term of an A.P.?
5. What is the significance of the common difference in an A.P.?
6. How would you find the number of terms in an A.P. given its first and last terms?
7. Can you solve an A.P. problem where the common difference is a fraction?
8. What happens when the common difference in an A.P. is negative?

**Tip:** When working with A.P.s, always verify the common difference by subtracting consecutive terms to ensure consistent results.

Learn how to find the 10th term in arithmetic progressions (A.P.) with examples including A.P.s like 5, 7, 9, 11 and more. Detailed step-by-step solutions provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation