alleryThe 10th term of an AP with first term $a = 5$ and common difference $d = 3$ is
A$30$
B$33$
C$35$
D$32$
Answer & Solution
Correct answer: D. $32$
1. AP formula: $a_n = a + (n-1)d$.
2. Substitute $a = 5$, $d = 3$, $n = 10$.
3. $a_{10} = 5 + (10-1)(3) = 5 + 9 \cdot 3 = 5 + 27 = 32$.
4. Quick verification by counting: starts at 5, add 3 nine times → 5+3=8, 11, 14, 17, 20, 23, 26, 29, 32. ✓
5. Option A uses $n$ instead of $(n-1)$. Option C overshoots by 1. Option D adds 30 instead of 27.
_Source: syllabus Mathematics, Ch 8, §8.2 + Examples, p. 3–4._
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