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The formula for the $n$th term of an AP with first term $a$ and common difference $d$ is
A$a_n = a + nd$
B$a_n = a + (n-1)d$
C$a_n = a + (n+1)d$
D$a_n = na + d$
Answer & Solution
Correct answer: B. $a_n = a + (n-1)d$
1. The nth term is a plus (n−1) steps of size d.
2. So $a_n = a + (n-1)d$.
3. (There are only n−1 gaps before the nth term, not n.)
_Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch1 'Arithmetic Progressions' (nth term)_
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