Question

Which is an equation for the nth terms of the sequence 12,15,18,21

Answer 1

`\bf 12~~,~~\stackrel{12+3}{15}~~,~~\stackrel{15+3}{18}~~,~~\stackrel{18+3}{21}~\hspace{10em}\stackrel{\textit{common difference}}{d=3} \\\\[-0.35em] ~\dotfill\\\\ n^(th)\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^(th)\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=12\\ d=3 \end{cases} \\\\\\ a_n=12+(n-1)3\implies a_n=12+3n-3\implies a_n=3n+9`

Answer 2

tₙ = 3(3 + n)

Explanation:

Points to remember

nth term of an AP

tₙ = a + (n - 1)d

Where a - first term of AP

d - Common difference of AP

To find the nth term

The given series is,

12,15,18,21 .....

Here a = 12 and d = 15 - 12 = 3

tₙ = a + (n - 1)d

= 12 + (n - 1)3

=12 + 3n - 3

= 9 + 3n

= 3(3 + n)

Therefore tₙ = 3(3 + n)