csat-suneung 2015 Q6

csat-suneung · South-Korea · csat__math-B 3 marks Geometric Sequences and Series Sum of an Infinite Geometric Series (Direct Computation)

For a geometric sequence $\left\{ a _ { n } \right\}$ with $a _ { 1 } = 3 , a _ { 2 } = 1$, what is the value of $\sum _ { n = 1 } ^ { \infty } \left( a _ { n } \right) ^ { 2 }$? [3 points]
(1) $\frac { 89 } { 8 }$
(2) $\frac { 87 } { 8 }$
(3) $\frac { 85 } { 8 }$
(4) $\frac { 83 } { 8 }$
(5) $\frac { 81 } { 8 }$

For a geometric sequence $\left\{ a _ { n } \right\}$ with $a _ { 1 } = 3 , a _ { 2 } = 1$, what is the value of $\sum _ { n = 1 } ^ { \infty } \left( a _ { n } \right) ^ { 2 }$? [3 points]\\
(1) $\frac { 89 } { 8 }$\\
(2) $\frac { 87 } { 8 }$\\
(3) $\frac { 85 } { 8 }$\\
(4) $\frac { 83 } { 8 }$\\
(5) $\frac { 81 } { 8 }$

Paper Questions

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