A sequence is defined by the general term for .

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

A sequence is defined by the general term

a_n = 5\cdot 2^{n-1} + 3

for

n \ge 1

. (i) Determine whether the sequence

\{a_n\}

forms an AP, a GP, or neither. Justify your answer by considering consecutive terms. (ii) If

\{a_n\}

is neither an AP nor a GP, define a new sequence

b_n = a_n - 3

and classify

\{b_n\}

accordingly. (iii) For the sequence

\{b_n\}

, write an expression for the 10th term and evaluate its numerical value.