9000063804
Level:
A
We are given the sequence \(\left (\log 10^{n}\right )_{n=1}^{\infty }\).
Find the product of the first five terms of this sequence.
\(120\)
\(0\)
\(5\)
\(6\)
Introduction to sequences
9000063807
Level:
A
Among the numbers \(5\),
\(15\),
\(28\),
\(47\)
identify the number which is not a member of the sequence
\(\left (2n^{2} - 3\right )_{n=1}^{\infty }\).
\(28\)
\(5\)
\(15\)
\(47\)
9000063808
Level:
B
Given the sequence \(\left (2n + 3\right )_{n=1}^{\infty }\),
find the recurrence relation for this sequence.
\(a_{n+1} = a_{n} + 2,\ a_{1} = 5\)
\(a_{n+1} = a_{n} + 3,\ a_{1} = 5\)
\(a_{n+1} = a_{n} + 4,\ a_{1} = 5\)
\(a_{n+1} = a_{n} + 5,\ a_{1} = 5\)
9000063809
Level:
B
Given the sequence \(\left ( \frac{1}
{n(n+1)}\right )_{n=1}^{\infty }\),
find the recurrence relation for this sequence.
\(a_{n+1} = \frac{n}
{n+2}a_{n},\ a_{1} = \frac{1}
{2}\)
\(a_{n+1} = \frac{n}
{n+1}a_{n},\ a_{1} = \frac{1}
{2}\)
\(a_{n+1} = \frac{n+1}
{n} a_{n},\ a_{1} = \frac{1}
{2}\)
\(a_{n+1} = \frac{n+1}
{n+2}a_{n},\ a_{1} = \frac{1}
{2}\)
9000063810
Level:
A
Consider the sequences \(\left (a_{n}\right )_{n=1}^{\infty }\)
and \(\left (b_{n}\right )_{n=1}^{\infty }\)
where \(a_{n} = 2^{n}\)
and \(b_{n} = n^{2} - 1\),
respectively. Identify a true statement in the terms of these sequences.
\(a_{3} = b_{3}\)
\(a_{2} = b_{2} + 2\)
\(a_{4} = b_{4} - 2\)
\(a_{5} = b_{5} - 8\)
9000063802
Level:
B
We are given the sequence \(\left (an + b\right )_{n=1}^{\infty }\).
This sequence satisfies \(a_{4} - a_{1} = 6\). Use
this information to find \(a\).
\(a = 2\)
\(a = -2\)
\(a = -1\)
\(a = 1\)
9000063806
Level:
B
Consider the sequence \(a_{n+1} = a_{n} - 2a_{n-1}\)
with \(a_{3} = 0\)
and \(a_{4} = -16\).
Find \(a_{2} - a_{1}\).
\(4\)
\(16\)
\(- 4\)
\(8\)
9000063805
Level:
A
Consider sequence \(a_{n+1} = 2a_{n} - a_{n-1}\)
with \(a_{1} = 3\)
and \(a_{2} = 5\).
Find \(a_{3} + a_{4}\).
\(16\)
\(12\)
\(0\)
\(- 2\)