Determine the Arithmetic Progression whose third term is 5 and the seventh term is 9.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3, 4, 5, 6, 7, ...
The \(n\)th term of an AP with first term \(a\) and common difference \(d\) is \(a_n=a+(n-1)d\), so each given term gives one equation.
Third term: \(a+2d=5\) (1)
Seventh term: \(a+6d=9\) (2)
Subtracting (1) from (2), \(a\) cancels: \(4d=4\), so \(d=1\)
From (1): \(a=5-2=3\)
The AP is 3, 4, 5, 6, 7, ...