Find the 10th term of the AP : 2, 7, 12, . . .
Step-by-Step Solution
Key Concept: Identify the first term \(a\) and the common difference \(d\) of the arithmetic progression, then use the nth‑term formula \(a_n = a + (n-1)d\).
1. First term: From the given AP, the first term \(a = 2\).
2. Common difference: \(d = 7-2 = 5\) (or \(12-7 = 5\)).
3. Nth‑term formula: For an AP, the \(n^{th}\) term is given by
$$a_n = a + (n-1)d.$$
4. Substitute \(n = 10\):
$$a_{10} = 2 + (10-1)\times 5$$
$$a_{10} = 2 + 9\times 5$$
$$a_{10} = 2 + 45$$
$$a_{10} = 47.$$
Correct Answer: 47