A geometric progression has first term and common ratio .

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

A geometric progression has first term

2

and common ratio

\dfrac{3}{2}

. (i) Write the expression for the sum of its first

n

terms,

S_{n}

. (ii) Set up an inequality to determine the least value of

n

for which

S_{n}

exceeds

1500

. (iii) Solve the inequality and state the least integer value of

n

that satisfies the given condition. (iv) Verify your answer by calculating

S_{n}

for the value of

n

obtained.