What is the fifth term of the sequence (2, 4, 8, 16, ...)?
Answer and explanation
Correct answer: 32
The governing concept is identifying the rule of a geometric sequence. Each displayed term is twice the preceding term: 2×2=4, 4×2=8, and 8×2=16. Continuing the same rule gives the fifth term as 16×2=32. Equivalently, the terms can be written as 2¹, 2², 2³, 2⁴, so the fifth term is 2⁵=32. Therefore option B is correct. Option A does not follow the repeated doubling pattern, option C is not produced by multiplying 16 by 2, and option D is the sixth term because 32×2=64. This check also shows why simply adding a fixed number would be inappropriate for this sequence.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The governing concept is identifying the rule of a geometric sequence. Each displayed term is twice the preceding term: 2×2=4, 4×2=8, and 8×2=16. Continuing the same rule gives the fifth term as 16×2=32. Equivalently, the terms can be written as 2¹, 2², 2³, 2⁴, so the fifth term is 2⁵=32. Therefore option B is correct. Option A does not follow the repeated doubling pattern, option C is not produced by multiplying 16 by 2, and option D is the sixth term because 32×2=64. This check also shows why simply adding a fixed number would be inappropriate for this sequence.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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