Question

The nth term of an AP is 6n+2 find the common difference.

Answer 1

Step-by-step explanation:

Hope this helps you.

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

The nth term of an AP is 6n + 2.

It means,

$\rm \: a_n = 6n + 2$

So,

$\rm \: a_1 = 6 \times 1 + 2$

$\rm \: = 6 + 2$

$\rm \: = 8$

$\rm \: a_2 = 6 \times 2 + 2$

$\rm \: = 12 + 2$

$\rm \: = 14$

So, Common difference of an AP series is

$\rm \: d = a_2 - a_1$

$\rm \: = \: 14 - 8$

$\rm \: = \: 6$

Hence,

$\rm\implies \:d \: = \: 6$

$\rule{190pt}{2pt}$

Remark :- Short Cut Trick

If nᵗʰ term of AP is a linear expression, i.e aₙ = an + b, then coefficient of n is always common difference.

As in given question, aₙ = 6n + 2, then common difference is 6

$\rule{190pt}{2pt}$

Additional Information :-

↝ nᵗʰ term of an arithmetic progression is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{a_n\:=\:a\:+\:(n\:-\:1)\:d}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

aₙ is the nᵗʰ term.

a is the first term of the progression.

n is the no. of terms.

d is the common difference.

↝ Sum of n  terms of an arithmetic progression is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{S_n\:=\dfrac{n}{2} \bigg(2 \:a\:+\:(n\:-\:1)\:d \bigg)}}}}}} \\ \end{gathered}$

Wʜᴇʀᴇ,

Sₙ is the sum of n terms of AP.

a is the first term of the progression.

n is the no. of terms.

d is the common difference.