A sequence ( T_n ) is defined as follows: • The odd–numbered terms (T_1, ,T_3, ,T_5,…
MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
A sequence {Tn} is defined as follows:
• The odd–numbered terms T1,T3,T5,… form an arithmetic progression whose first term is 2 and common difference is 3.
• The even–numbered terms T2,T4,T6,… form a geometric progression whose first term is 4 and common ratio is 2.
Answer the following questions.
(i) Write the first six terms of the sequence.
(ii) Obtain a single formula for the general term Tn valid for all positive integers n.
(iii) Find the sum of the first ten terms of the sequence.