Question

Determine the next term in the sequence: 3, 6, 9, … 12 15 18 27

Answer 1

Answer:

12

Step-by-step explanation:

multiplication of 3

Answer 2

Option (A)  

Answer:

The next term in the sequence 3, 6, 9, …  is 12

Solution:

Given sequence is 3, 6, 9,…

Let say first term $a_{1}=3$

Second term $a_{2} = 6$

And third term $a_{3} = 9$

Now let’s determine the common difference ‘d’ that is

$\mathrm{d}=\mathrm{a}_{2}-\mathrm{a}_{1}=6-3=3$

$\mathrm{d}=\mathrm{a}_{3}-\mathrm{a}_{2}=9-6=3$

Since $\mathrm{a}_{2}-\mathrm{a}_{1}=\mathrm{a}_{3}-\mathrm{a}_{2}=3$

so given series is arithmetic progressions. We need next term that is $a_{4}$

Formula of nth term of AP is as follows,

$a_{n}=a_{1}+(n-1) d$

So fourth term is when n = 4,

$\mathrm{a}_{4}=3+(4-1) \times 3$

$\mathrm{a}_{4}=3+3 \times 3$

$a_{4}=3+9=12$

So next term of given sequence is 12. Hence option (A) is correct.