Arithmetic Sequences

9000065301

Level: 
A
Find the recurrence equations for the arithmetic sequence with the first term \(a_{1} = 4\) and the common difference \(d = -2\).
\(a_{1} = 4,\ a_{n+1} = a_{n} - 2,\ n\in\mathbb{N}\)
\(a_{1} = 4,\ a_{n+1} = a_{1} - 2,\ n\in\mathbb{N}\)
\(a_{n} = 4 + a_{n+2},\ n\in\mathbb{N}\)
\(a_{n+1} = a_{n} + 2,\ n\in\mathbb{N}\)

9000065303

Level: 
A
Find the recurrence equations for the arithmetic sequence with the second term \(a_{2} = 7\) and the common difference \(d = 4\).
\(a_{1} = 3,\ a_{n} = a_{n-1} + 4,\ n\in\mathbb{N}\)
\(a_{1} = 7,\ a_{n+1} = a_{n} + 4,\ n\in\mathbb{N}\)
\(a_{n} = 7 + a_{n+4},\ n\in\mathbb{N}\)
\(a_{n+1} = a_{n} + 7,\ n\in\mathbb{N}\)

9000064801

Level: 
C
The sides of a right triangle form three consecutive terms of an arithmetic sequence. The perimeter of the triangle is \(60\, \mathrm{cm}\). Find the hypotenuse of the triangle (the longest side).
\(25\, \mathrm{cm}\)
\(12\, \mathrm{cm}\)
\(15\, \mathrm{cm}\)
\(20\, \mathrm{cm}\)
\(30\, \mathrm{cm}\)