(a) The sum of the first terms of progression is given by . (i) Find , the term of…

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

(a) The sum of the first

n

terms of progression is given by

S_n = \frac{1}{2} \left( \frac{5}{3} \right)^n - \frac{1}{2}

. (i) Find

u_n

, the

n^{\text{th}}

term of the progression. (ii) Determine if

u_1, u_2, u_3, u_4, \dots

is a geometric progression. (b) Given the sum of the first

n

terms of another sequence,

\{v_n\}

\frac{1}{2} \left( \frac{5}{3} \right)^n

. By considering

v_1

, justify if

\{v_n\}

is a geometric progression.