MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Two progressions have the same first term 3.
• Progression A is an arithmetic progression with common difference 2.
• Progression B is a geometric progression with common ratio 2.
Use this information to answer the following.
(i) Write the nth term of each progression.
(ii) Find the positive integer n for which the nth terms of the two progressions are equal.
(iii) For the value of n found in part (ii), compare the sums of the first n terms of the two progressions and state which sum is greater.