Mathematics

Problem

A geometric progression has first term

2

and common ratio

\dfrac{3}{2}

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

n

terms,

S_{n}

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

n

for which

S_{n}

exceeds

1500

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

n

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

S_{n}

for the value of

n

obtained.