Arithmetic sequences

9000065302

Level:

Find the formula for the $n$-th term of an arithmetic sequence with the first term $a_{1} = 1$ and the second term $a_{2} = -2$.

$a_{n} = 4 - 3n,\ n\in\mathbb{N}$

$a_{n} = 1 - 2n,\ n\in\mathbb{N}$

$a_{n} = -2 + n,\ n\in\mathbb{N}$

$a_{n} = 3 + 2n,\ n\in\mathbb{N}$

9000065303

Level:

Find the recurrence equations for the arithmetic sequence with the second term $a_{2} = 7$ and the common difference $d = 4$.

$a_{1} = 3;\ a_{n} = a_{n-1} + 4,\ n\in\mathbb{N}$

$a_{1} = 7;\ a_{n+1} = a_{n} + 4,\ n\in\mathbb{N}$

$a_{n} = 7 + a_{n+4},\ n\in\mathbb{N}$

$a_{n+1} = a_{n} + 7,\ n\in\mathbb{N}$

9000065304

Level:

Find the first term $a_{1}$ and the common difference $d$ of the arithmetic sequence $(5 + 2n)_{n=1}^{\infty }$.

$a_{1} = 7;\ d = 2$

$a_{1} = 5;\ d = 2$

$a_{1} = 3;\ d = -2$

$a_{1} = 2;\ d = 5$

9000065307

Level:

In the arithmetic sequence given by the first term $a_{1} = 4$ and the common difference $d = 2$ find the sum of the first twelve terms of the sequence.

$s_{12} = 180$

$s_{12} = 72$

$s_{12} = 120$

$s_{12} = 168$

9000065308

Level:

For the arithmetic sequence with the first term $a_1=3$ holds $a_n=27$ and the sum of the first $n$ terms is $195$. Find $n$.

$n = 13$

$n = 14$

$n = 15$

$n = 16$

9000060609

Level:

Identify the real number $x$ which ensures that the numbers $a_{1} =\log (x + 2)$, $a_{2} =\log (3x + 6)$ and $a_{3} =\log 18$ are three consecutive terms of an arithmetic sequence.

$x = 0$

$x =\log 3$

$x = 3$

$x = 8$

$x = 18$

9000060603

Level:

Identify the real number $x$ which ensures that the numbers $a_{1} = -x$, $a_{2} = -5$ and $a_{3} = 0$ are three consecutive terms of an arithmetic sequence.

$x = 10$

$x = 0$

$x = -5$

$x = 5$

$x = -10$

9000060606

Level:

Identify the real number $x$ which ensures that the numbers $a_{1} = 5x + 1$, $a_{2} = x$ and $a_{3} = 7x + 3$ are three consecutive terms of an arithmetic sequence.

$x = -0.4$

$x = 0.4$

$x = 2.5$

$x = -2.5$

$x = 5$

9000060610

Level:

Identify the real number $x$ which ensures that the numbers $a_{1} =\log x$, $a_{2} = 2$ and $a_{3} =\log x^{3}$ are three consecutive terms of an arithmetic sequence.

$x = 10$

$x = 0$

$x = 0.1$

$x = 1$

$x = -1$

9000060602

Level:

Identify the real number $x$ which ensures that the numbers $a_{1} = -12$, $a_{2} = x$ and $a_{3} = 24$ are three consecutive terms of an arithmetic sequence.

$x = 6$

$x = 0$

$x = 12$

$x = -24$

$x = -2$

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