Question

Determine the next term in the sequence: 3, 6, 9, …

12
15
18
27

Answer 1

12

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) * 3`

`\mathrm{a}_(4)=3+3 * 3`

`a_(4)=3+9=12`

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