Find a20 of a geometric sequence if the first few terms of the sequence are given by −12,14,−18,116,⋯
[ 2 marks ]
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Solution
We first use the first few terms to find the common ratio. r=a2a1=14−12=−12 r=a3a2=−1814=−12 r=a4a3=116−18=−12
The common ratio r=−12. [ 1 mark ]
We now use the formula an=a1×rn−1 for the nth term to find a20 as follows. a20=a1×r20−1 =(−12)×(−12)20−1 =12020
[ 1 mark ]