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 [tex]a_{1}=3[/tex]
Second term [tex]a_{2} = 6[/tex]
And third term [tex]a_{3} = 9[/tex]
Now let’s determine the common difference ‘d’ that is
[tex]\mathrm{d}=\mathrm{a}_{2}-\mathrm{a}_{1}=6-3=3[/tex]
[tex]\mathrm{d}=\mathrm{a}_{3}-\mathrm{a}_{2}=9-6=3[/tex]
Since [tex]\mathrm{a}_{2}-\mathrm{a}_{1}=\mathrm{a}_{3}-\mathrm{a}_{2}=3[/tex]
so given series is arithmetic progressions. We need next term that is [tex]a_{4}[/tex]
Formula of nth term of AP is as follows,
[tex]a_{n}=a_{1}+(n-1) d[/tex]
So fourth term is when n = 4,
[tex]\mathrm{a}_{4}=3+(4-1) \times 3[/tex]
[tex]\mathrm{a}_{4}=3+3 \times 3[/tex]
[tex]a_{4}=3+9=12[/tex]
So next term of given sequence is 12. Hence option (A) is correct.
