Question

The nth term of a sequence is: 2n + 6.What is the 12th term in the sequence?

Answer 1

Answer:

Answer is 30

Step-by-step explanation:

2(12)+6=30

Answer 2

The 12th term in the sequence is n = 30

Step-by-step explanation:

Given, $\sf{t_n\:=\:2n\:+\:6}$

Firstly, let's substitute values for ${'n'}$ to find the first term ${a}$ and common difference ${d}$.

When $\sf{n\:=\:1}$,

$\sf⟹{t_1\:=\:2(1)\:+\:6}$

$\sf⟹{t_1\:=\:2\:+\:6}$

$\sf⟹{t_1\:=8}$

When $\sf{n\:=\:2}$,

$\sf⟹{t_2\:=\:2(2)\:+\:6}$

$\sf⟹{t_2\:=\:4\:+\:6}$

$\sf⟹{t_2\:=10}$

When $\sf{n\:=\:3}$,

$\sf⟹{t_3\:=\:2(3)\:+\:6}$

$\sf⟹{t_3\:=\:6\:+\:6}$

$\sf⟹{t_3\:=12}$

Let the sequence be, $\sf{t_1\:=\:8,\:t_2\:=\:10,\:t_3\:=\:12}$ ....

From this we could find,

• First term ${a}$ = 8
• Common Difference ${d}$= $\sf{t_2\:-\:t_1}$ = $\sf{10\:-\:8}$ = $\sf{2}$

Finding 12 th term :

$\sf⟹{n\:=\:a\:+\:(n\:-\:1)\:d}$

$\sf⟹{n\:=\:8\:+\:(12\:-\:1)\:2}$

$\sf⟹{n\:=\:8\:+\:(11)\:2}$

$\sf⟹{n\:=\:8\:+\:(11)\:2}$

$\sf⟹{n\:=\:8\:+\:22}$

$\sf⟹{n\:=30}$

Hence, 12th term in the sequence n = 30.