Find the indicated terms in each of the following sequences whose $n$ th terms are $a_{n} = (n - 1) (2 - n) (3 + n); a_{1}, a_{2}, a_{3}$

Open in App

Solution

The $n^{t h}$ term of the sequence is

$a_{n} = (n - 1) (2 - n) (3 + n) . . . . . . . . . . . . . . . . . . . e q (1)$

1) To find the first term of sequence $(a_{1})$ put n=1 in eq(1)
$⟹ a_{1} = (1 - 1) (2 - 1) (3 + 1)$
$⟹ a_{1} = 0 \times 1 \times 4$
$⟹ a_{1} = 0$

2)To find the second term of sequence $(a_{2})$ put n=2 in eq(1)
$⟹ a_{2} = (2 - 1) (2 - 2) (3 + 2)$
$⟹ a_{2} = 1 \times 0 \times 5$
$⟹ a_{2} = 0$

3)To find the third term of sequence $(a_{3})$ put n=3 in eq(1)
$⟹ a_{3} = (3 - 1) (2 - 3) (3 + 3)$
$⟹ a_{3} = 2 \times - 1 \times 6$
$⟹ a_{3} = - 12$

Suggest Corrections

Similar questions

a_{n} = \frac{3 n - 2}{4 n + 5}; a_{7} a n d a_{8}

n

a_{n} = {(- 1)}^{n} n; a_{3}, a_{5}, a_{8}

n

a_{n} = n (n - 1) (n - 2); a_{5}

a_{8}

n

a_{n} = 5 n - 4; a_{12}

a_{15}

n

a_{n} = \frac{3 n - 2}{4 n + 5}; a_{7}

a_{8}

Join BYJU'S Learning Program