Geometric sequences and seriesEdexcel A-Level Maths: Mind map

Exam questions on Geometric sequences and series

1. A geometric sequence has first term $64$ and common ratio $\frac34$.
   Find the least value of $n$ for which the $n$th term is less than $1$.2 marks
2. A geometric series has second term $12$ and fifth term $324$.
   Find the sum of the first $8$ terms.2 marks
3. A geometric series has first term $a$ and common ratio $r$, where $r\ne1$.
   Prove that the sum of the first $n$ terms is $S_n=\frac{a(1-r^n)}{1-r}$.3 marks