1.11 Sum of infinite geometric sequencesIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 1.11 Sum of infinite geometric sequences

1. A geometric sequence has first term $u_1=12$ and common ratio $r=\frac13$.
   Use your GDC to find the least value of $n$ for which the sum of the first $n$ terms is greater than $17.9$.2 marks
2. A ball is dropped from a height of $2$ m onto a hard floor. After each bounce it rises to $80\%$ of the height from which it last fell.
   Use your GDC to find the number of the first bounce after which the ball rises to less than $0.1$ m.2 marks
3. The recurring decimal $0.272727\ldots$ can be written as the sum of an infinite geometric series.
   Write down the first term and the common ratio of the series $0.27+0.0027+0.000027+\ldots$, and explain why its sum to infinity exists.3 marks