Consider the arithmetic sequence whose -th term is
MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series
Problem
Consider the arithmetic sequence whose k-th term is 4+(k−1)⋅3. Answer the following questions.
(i) Write the sum of its first n terms using summation (sigma) notation with index starting at k=1.
(ii) Rewrite the same sum using index starting at k=0, clearly indicating the new general term and the revised limits of summation.
(iii) Explain, in not more than three sentences, why the two sigma forms obtained in parts (i) and (ii) represent the same quantity.