The next term in the sequence: 3, 6, 12, … is 24. This can be obtained by finding the nth term and finding the 4th term.
What is a sequence ?
A collection of items in a particular order and repetitions are allowed.
a, a+d, a+2d, ..., a+(n-1)d, where a is the first term, d is the common difference and a+(n-1)d is the nth term.
a, ar, ar¹, ..., arⁿ⁻¹, where a is the first term, r is the common ratio and arⁿ⁻¹ is the nth term.
What is the next term ?
Given that, 3, 6, 12, …⇒this is a Geometric Sequence with nth term,
aₙ=3rⁿ⁻¹, n=1,2,3,...
From the given sequence, a₁=3, r=2
- when n=1, a₁=3(r¹⁻¹)=3(r⁰)=3(2⁰)=3×1=3
- when n=2, a₂=3(r²⁻¹)=3(r¹)=3(2¹)=3×2=6
- when n=3, a₃=3(r³⁻¹)=3(r²)=3(2²)=3×4=12
- when n=4, a₄=3(r⁴⁻¹)=3(r³)=3(2³)=3×8=24
Hence the next term in the sequence: 3, 6, 12, … is 24. Thus option C is the correct answer.
Learn more about sequences here:
brainly.com/questions/2959141
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