Let a sequence be defined by $a_{1} = 3, a_{n} = 3 a_{n - 1} + 1$ for all $n > 1$ .
Find the first four terms of the sequence.

Open in App

Solution

We have, $a_{1} = 3$

and, $a_{n} = 3 a_{n - 1} + 1$ for all $n > 1$ .
Putting $n = 2, 3$ and $4$ , we get

$a_{2} = 3 a_{1} + 1 = 3 \times 3 + 1 = 10$

$a_{3} = 3 a_{2} + 1 = 3 \times 10 + 1 = 31$

and, $a_{4} = 3 a_{3} + 1 = 3 \times 31 + 1 = 94$
Hence, the first four terms of sequence are $3, 10, 31$ and $94$ .

Suggest Corrections

Similar questions

Find the first four terms of the sequence defined by $a_{1} = 3$ and $a_{n} = 3 a_{n - 1} + 2$ , for all n > 1.

a_{1} = 3, a_{n} = 3 a_{n - 1} + 2

n > 1

a_{1} = 3, a_{n} = 3 a_{n - 1} + 2

n > 1

a_{n} = 3 a_{n - 1} - a_{n - 2}

n > 2

a_{5}

a_{1} = 4

a_{2} = 3

Join BYJU'S Learning Program