Geometric sequences & series

Given the geometric series: 9 + 3 + 1 + … Explain why the sum to infinity exists, and calculate S∞.

Given the geometric sequence: 6; 18; 54; … Determine $(a)T_{8}$, and $(b)S_{8}$.

Given the geometric series: $4+1+\tfrac{1}{4}+$ … Explain why the sum to infinity exists, and calculate S∞.

Given the geometric series: 4 + 2 + 1 + … Explain why the sum to infinity exists, and calculate S∞.

Given the geometric sequence: 7; 14; 28; … Determine $(a)T_{7}$, and $(b)S_{7}$.

Given the geometric sequence: 8; 16; 32; … Determine $(a)T_{6}$, and $(b)S_{6}$.

Given the geometric sequence: 5; 10; 20; … Determine $(a)T_{6}$, and $(b)S_{6}$.

Given the geometric sequence: 7; 14; 28; … Determine $(a)T_{8}$, and $(b)S_{8}$.

Given the geometric series: 8 + 4 + 2 + … Explain why the sum to infinity exists, and calculate S∞.

Given the geometric sequence: 4; 8; 16; … Determine $(a)T_{6}$, and $(b)S_{6}$.

Given the geometric series: $12+3+\tfrac{3}{4}+$ … Explain why the sum to infinity exists, and calculate S∞.

Given the geometric sequence: 2; 6; 18; … Determine $(a)T_{8}$, and $(b)S_{8}$.