To find the 21st term of the arithmetic progression (AP), we can use the formula for the $n$-th term of an AP:

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

Where:

• $T_n$ is the $n$-th term,
• $a$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

Step 1: Identify the first term $a$ and the common difference $d$.

• The first term $a = -3$,
• The second term $T_2 = 4$.

Now, to find the common difference $d$, we can use:

$d = T_2 - a = 4 - (-3) = 4 + 3 = 7$

Step 2: Find the 21st term.

Using the formula $T_n = a + (n - 1) \cdot d$, with $n = 21$:

$T_{21} = -3 + (21 - 1) \cdot 7$ $T_{21} = -3 + 20 \cdot 7$ $T_{21} = -3 + 140$ $T_{21} = 137$

Thus, the 21st term is 137.

Answer:

Option B: 137

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Would you like more details or have any questions? Here are 5 related questions to explore further:

1. How do you derive the formula for the $n$-th term of an arithmetic progression?
2. Can you find the sum of the first 21 terms of this AP?
3. How would you determine the common difference if only given the first and last term?
4. What is the significance of the common difference in an AP?
5. How does an arithmetic progression differ from a geometric progression?

Tip: In an AP, the common difference remains constant between consecutive terms. This makes it easy to predict future terms using the first term and the common difference.