Question

3. Consider the sequence 3, 6, 9, 12, 15, ..
(1) Write down the next two terms of
the sequence.
(ii) Find, in terms of n, a formula for the
nth term of the sequence.
(iii) Hence, find the 105th term.​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

The given sequence is

$3, 6, 9, 12, 15,...............$

Let $\{ \:a_n \} \:$be the given sequence

First Term = 3

Common Difference = 6 - 3 = 3

So the General Term

$= {n}^{th} \: \: term$

$\: = a_n$

$= 3 + (n - 1) \times 3$

$= 3n \: \: \: \: \: where \: \: n \in \mathbb{N}$

1. Next two Terms are

$a_6 = 3 \times 6 = 18$

$a_7 = 3 \times 7 = 21$

2. The formula for the nth term of the sequence$\: = a_n = 3n$

3.

${105}^{th \:} term \: = a_</strong><strong>{</strong><strong>105</strong><strong>}</strong><strong> = 3 \times 105 = 315$