Finding the nth Term of a Geometric SequenceGiven a geometric sequence with the first term a1 and the common ratio r , the nth (or general) term is given by Example 1: Find the 6th term in the geometric sequence 3,12,48,... . a1=3, r=123=4a6=3461=345=3072 Example 2: Find the 7th term for the geometric sequence in which a2=24 and a5=3 . Substitute 24 for a2 and 3 for a5 in the formula an=a1rn1 . a2=a1r2124=a1ra5=a1r51 3=a1r4 Solve the firstequation for a1 : a1=24r Substitute this expression for a1 in the second equation and solve for r . 3=24rr43=24r318=r3sor=12 a7=48(12)71=48164=34 See also: sigma notation of a series and nth term of a arithmetic sequence |
How to find geometric sequence
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