The image contains a problem that asks, "How many terms are there in the AP?"

It appears to show an arithmetic progression (AP) starting with terms:

$7, 10, 13, \dots, 43$

This is an arithmetic sequence where:

• The first term $a = 7$,
• The common difference $d = 10 - 7 = 3$,
• The last term $l = 43$.

The formula for the $n$-th term of an arithmetic progression is:

$a_n = a + (n - 1) \cdot d$

Substitute the known values:

$43 = 7 + (n - 1) \cdot 3$

We now solve for $n$.

$43 - 7 = (n - 1) \cdot 3$ $36 = (n - 1) \cdot 3$ $n - 1 = \frac{36}{3} = 12$ $n = 12 + 1 = 13$

So, there are 13 terms in this arithmetic progression.

Would you like further details, or do you have any questions?

Here are some related questions to explore:

1. How do you derive the formula for the $n$-th term of an AP?
2. What is the sum of the first $n$ terms in this AP?
3. Can an arithmetic progression have a non-integer common difference?
4. How does an arithmetic progression differ from a geometric progression?
5. How can we calculate the mean of all the terms in this AP?

Tip: In an arithmetic progression, the number of terms can easily be found if you know the first term, the common difference, and the last term using the formula for the $n$-th term.