alleryStart learning →In an AP, the 3rd term is 12 and the 7th term is 24. The first term $a$ and common difference $d$ are
A$a=8,\ d=2$
B$a=6,\ d=2$
C$a=9,\ d=3$
D$a=6,\ d=3$
Answer & Solution
Correct answer: D. $a=6,\ d=3$
1. Write both terms: $a_3 = a + 2d = 12$ and $a_7 = a + 6d = 24$.
2. Subtract the first from the second: $(a+6d)-(a+2d) = 24-12$, i.e. $4d = 12$, so $d = 3$.
3. Substitute back: $a + 2(3) = 12 \Rightarrow a = 6$. Check: $a_7 = 6 + 6(3) = 24$ ✓. So $a=6,\ d=3$.
_Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch1 'Arithmetic Progressions' (two-equation method)_
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