A sequence is to be formed by placing four arithmetic means between the numbers and…
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
A sequence is to be formed by placing four arithmetic means between the numbers 5 and 41 so that all six numbers together constitute an arithmetic progression.
(i) Find the common difference of the resulting progression.
(ii) Write down all six terms of the progression in order.
(iii) Determine the sum of all eight terms that would be obtained if two additional terms, one preceding 5 and one succeeding 41, are written so that the common difference found in part (i) is preserved for the extended progression.