How many terms are there in the Arithmetic Progression given below?
7, 13, 19, ..., 205
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 34
The terms of an arithmetic progression go up by the same common difference, and the \(n\)th term is \(a+(n-1)d\). Setting it equal to the last term gives an equation whose solution is the number of terms.
First term \(a=7\), common difference \(d=13-7=6\), last term 205
The last term is the \(n\)th term: \(7+(n-1)\times6=205\)
\((n-1)\times6=198\) and \(n-1=33\), so the progression has \(n=34\) terms