A sequence is arranged so that the odd-numbered terms form an arithmetic progression…
MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
A sequence (an) is arranged so that the odd-numbered terms form an arithmetic progression while the even-numbered terms form a geometric progression.
The first term is a1=2 and the second term is a2=3. Further, the common difference of the arithmetic progression is 2 and the common ratio of the geometric progression is 2. Answer the following questions.
(i) Write an explicit formula for an separately for odd n and even n.
(ii) Obtain an expression for the sum of the first n odd-numbered terms and for the sum of the first n even-numbered terms.
(iii) Hence calculate the sum of the first 10 terms of the sequence.