which term of an AP -8,3,14,25... will be 143 more than its 69th term 

We are given an arithmetic progression (AP) with the first few terms as: -8, 3, 14, 25, ...

The general formula for the \( n \)-th term \( T_n \) of an AP is:

\[
T_n = a + (n - 1) \cdot d
\]

where:
- \( a \) is the first term of the AP,
- \( d \) is the common difference,
- \( n \) is the term number.

### Step 1: Find the common difference \( d \)

We can find the common difference \( d \) by subtracting the first term from the second term:

\[
d = 3 - (-8) = 3 + 8 = 11
\]

Thus, the common difference \( d = 11 \).

### Step 2: Write the formula for the 69th term

The 69th term \( T_{69} \) is:

\[
T_{69} = a + (69 - 1) \cdot d
\]
\[
T_{69} = -8 + 68 \cdot 11
\]
\[
T_{69} = -8 + 748 = 740
\]

Thus, the 69th term \( T_{69} = 740 \).

### Step 3: Set up the equation for the unknown term

We are told that a certain term of the AP is 143 more than the 69th term. Let this unknown term be the \( n \)-th term. The equation is:

\[
T_n = T_{69} + 143
\]
\[
T_n = 740 + 143 = 883
\]

### Step 4: Use the general formula for the \( n \)-th term

The \( n \)-th term is given by:

\[
T_n = a + (n - 1) \cdot d
\]
Substitute the known values of \( T_n = 883 \), \( a = -8 \), and \( d = 11 \):

\[
883 = -8 + (n - 1) \cdot 11
\]
\[
883 + 8 = (n - 1) \cdot 11
\]
\[
891 = (n - 1) \cdot 11
\]
\[
n - 1 = \frac{891}{11} = 81
\]
\[
n = 81 + 1 = 82
\]

### Conclusion:
The 82nd term of the AP will be 143 more than the 69th term.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the common difference in an arithmetic progression?
2. What is the formula for the sum of the first \( n \) terms of an AP?
3. How can you check if a sequence is arithmetic?
4. How do you find the \( n \)-th term of a geometric progression?
5. What is the difference between arithmetic and geometric progressions?

**Tip:** In an arithmetic progression, the difference between consecutive terms is always constant.

Which term of an AP -8,3,14,25... will be 143 more than its 69th term?

Discover how to find the term of an arithmetic progression (AP) where the term is 143 more than the 69th term. This problem covers key concepts like the general term formula for AP and finding the common difference, suitable for students in Grades 9-11.

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