The 21st and 33rd terms of an arithmetic progression are 91 and 145 respectively. What is the 29th term?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 127
In an arithmetic progression each term is the one before plus the common difference \(d\), so two terms that are \(n\) places apart differ by \(nd\).
The 33rd term is 12 places after the 21st: \(12d=145-91=54\), so \(d=4.5\)
The 29th term is 8 places after the 21st: \(91+8\times4.5=91+36=127\)