In an arithmetic progression, if 6 is the third term, the ninth term exceeds the seventh term by 3, then 12 is which term?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Seventh
In an arithmetic progression the \(n\)th term is \(a+(n-1)d\), where \(a\) is the first term and \(d\) the common difference. Two terms that are two places apart differ by \(2d\).
Finding \(d\) and \(a\) (the 9th term is 3 more than the 7th; the 3rd term is 6):
\(2d=3\), so \(d=1.5\)
\(a+2d=6\), so \(a=6-3=3\)
The term equal to 12:
\(3+(n-1)\times1.5=12\)
\((n-1)\times1.5=9\), so \(n-1=6\)
\(n=7\): 12 is the seventh term (3, 4.5, 6, 7.5, 9, 10.5, 12)