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Subjects
Mathematics State Board
Class 10
Numbers and Sequences
Sequences

5. Two marks exercise problems II

Exercise condition:

12 m.

1. Find the first four terms of the sequences whose $n^{\text{th}}$ terms are given by

(i) $a_n = n^3 - 2$.

$-1$, $3$, $12$ and $25$
$1$, $8$, $27$ and $64$
$-1$, $6$, $25$ and $62$
$1$, $6$, $52$ and $62$

(ii) $a_n = (-1)^{n + 1} n (n + 1)$

$-2$, $-10$, $28$ and $-42$
$2$, $-8$, $16$ and $-32$
$2$, $-6$, $12$ and $-20$
$-2$, $8$, $-12$ and $20$

(iii) $a_n = 2n^2 - 6$

$-4$, $2$, $12$ and $26$
$4$, $8$, $16$ and $38$
$4$, $-1$, $-12$ and $-26$
$-4$, $-12$, $-26$ and $-52$

2. Find the $n^{\text{th}}$ term of the following sequences.

(i) $2$, $5$, $10$, $17$, ...

$n^{2} + 1$
$n + 1$
$2 n^{2} + 1$
$n^{2} - 1$

(ii) $0$, $\frac{1}{2}$, $\frac{2}{3}$, ...

$\frac{n + 1}{n}$
$\frac{n - 1}{n}$
$n^{2} - \frac{1}{n}$
$n - \frac{1}{n}$

(iii) $3$, $8$, $13$, $18$, ...

$5 n + 2$
$n + 2$
$5 n - 2$
$2 n + 1$

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