A geometric sequence has a first term of 2 and a common ratio of 1.05. Find the value of the smallest term which is greater than 500.

$2 \times {1.05^{n - 1}} > 500$     M1

$n - 1 > \frac{{\log {\text{ }}250}}{{\log {\text{ }}1.05}}$     M1

$n - 1 > 113.1675…$     A1

$n = 115$     (A1)

${u_{115}} = 521$     A1     N5

Note: Accept graphical solution with appropriate sketch.

[5 marks] 

Many candidates misread the question and stopped at showing that the required term was the ${115^{{\text{th}}}}$.