Geometric sequences

1003107308

Level: 
A
The first five terms of a geometrical sequence are: \( -2,\ 1,\,-\frac12,\ \frac14,\,-\frac18 \). Find the recursive formula of this sequence.
\( a_1=-2\,;\ a_{n+1}=a_n\cdot\left(-\frac12\right),\ n\in\mathbb{N} \)
\( a_1=-2\,;\ a_{n+1}=a_n\cdot\left(-\frac14\right),\ n\in\mathbb{N} \)
\( a_1=-2\,;\ a_{n+1}=a_n\cdot\frac12,\ n\in\mathbb{N} \)
\( a_1=-2\,;\ a_{n+1}=a_n\cdot\left(-\frac12\right)^n,\ n\in\mathbb{N} \)

9000073007

Level: 
B
Consider a geometric sequence \((a_{n})_{n=1}^{\infty }\). Let \(q\) be the quotient and \(s_{n}\) be the sum of the first \(n\) terms. Given \(a_{1} = -1\: 000\) and \(a_{2} = 100\), find the sum of the first four terms of the sequence.
\(s_{4} = -909\)
\(s_{4} = -900\)
\(s_{4} = 911\)
\(s_{4} = -911\)

9000073006

Level: 
B
Consider a geometric sequence \((a_{n})_{n=1}^{\infty }\). Let \(q\) be the quotient and \(s_{n}\) be the sum of the first \(n\) terms. Given \(a_{1} = 1\) and \(a_{4} = -8\), find the sum of the first five terms of the sequence.
\(s_{5} = 11\)
\(s_{5} = 31\)
\(s_{5} = 16\)
\(s_{5} = -16\)

9000073001

Level: 
B
Consider a geometric sequence \((a_{n})_{n=1}^{\infty }\). Let \(q\) be the quotient and \(s_{n}\) be the sum of the first \(n\) terms. Given \(a_{1} = 2\) and \(q = 2\), find the sum of the first five terms of the sequence.
\(s_{5} = 62\)
\(s_{5} = 18\)
\(s_{5} = 32\)
\(s_{5} = -59\)

9000073002

Level: 
B
Consider a geometric sequence \((a_{n})_{n=1}^{\infty }\). Let \(q\) be the quotient and \(s_{n}\) be the sum of the first \(n\) terms. Given \(a_{6} = 5\) and \(q = 1\), find the sum of the first five terms of the sequence.
\(s_{5} = 25\)
\(s_{5} = 31\)
\(s_{5} = 6\)
\(s_{5} = 30\)