Find terms and sums of geometric progressions, where each term is multiplied by a constant common ratio.
In a GP, aₙ=a×r^(n−1), where a is the first term and r is the common ratio.
Find the 6th term of the GP 2, 6, 18, 54, ...
a=2, r=3; a₆=2×3⁵=2×243=486
Find the common ratio if the first term is 4 and the 4th term is 108.
108=4×r³; r³=27; r=3
Sₙ=a(rⁿ−1)/(r−1) for r≠1. This formula finds the sum of the first n terms of a geometric progression.
Find the sum of the first 5 terms of the GP 3, 6, 12, 24, ...
S₅=3(2⁵−1)/(2−1)=3×31=93
Find the sum of the first 4 terms of the GP 1, 3, 9, 27, ...
S₄=1(3⁴−1)/(3−1)=80/2=40
1. Find the 5th term of the GP 5, 10, 20, 40, ...
2. Find r if the first term is 3 and the 5th term is 48.
3. Find the sum of the first 6 terms of the GP 2, 4, 8, 16, ...
4. Find the sum of the first 3 terms of the GP 5, 15, 45, ...
5. A GP has first term 7 and common ratio 1/2. Find the 4th term.