Question

The Nth term of a sequence 3,6,9,12.... is?

Answer 1

Given,

A sequence 3,6,9,12...

To find,

The nth term of the sequence

Solution,

The first term of the given sequence is 3 and the second term is 6.

Let us first calculate the common difference between the term.

If a1, a2 ,a3, a4 are in sequence the common difference is calculated by a2-a1, a3-a2,  a4-a3.

Therefore, the common difference of the sequence 3,6,8,12... is

6 - 3 = 3,   9 - 6 = 3,   12 - 9 = 3.

Since, the common difference are equal so its clear that the given sequence is an Arithmetic Expression.

The nth term of the AP is an  = a + (n-1)d

a = 3 and d = 3 where a  is first term of an AP and d is common difference of an AP.

⇒   an  = a + (n-1)d

⇒   an = 3 + (n-1)3

⇒   an = 3 + 3n - 3

⇒  an = 3n.

Hence, nth term of the sequence, 3,6,9,12... is an = 3n.

Answer 2

Answer:

The $n^{th}$ term of the sequence is $3n.$

Step-by-step explanation:

Given, the sequence is $3,6,9,12,.... is$

Find: $n^{th}$ term of the sequence.

Solution:

Arithmetic progression: A sequence of numbers in which each differs from the preceding one by a constant quantity.

The given sequence is $3,6,9,12,...$

$a=3, d=6-3=3$

So, the $n^{th}$ term of the AP is

$a_n=a+(n-1)d$

$=3+(n-1)3$

$a_n=3+3n-3$

$a_n=3n$

Hence, $n^{th}$ term of the sequence is $3n.$

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