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

Question

asked May 5, 2020 71.5k views

2 Answers

Samer Ayoub · Answer 1 · 2020-05-11T10:24:47+0000

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.