Question:
Which of the following is an arithmetic sequence?
Which of the following is an arithmetic sequence?
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To quickly identify an arithmetic sequence, check if the difference between consecutive terms remains the same.
Updated On: Apr 21, 2026
- \(1, 4, 9, 16, 25\)
- \(3, 5, 7, 9, 11\)
- \(2, 4, 8, 16, 32\)
- \(1, 2, 4, 8, 16\)
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The Correct Option is B
Solution and Explanation
Concept:
An arithmetic sequence is one in which the difference between consecutive terms is constant.
Step 1: Check Option (A).
\[ 4-1=3,\quad 9-4=5,\quad 16-9=7 \] Differences are not constant.
Not an arithmetic sequence.
Step 2: Check Option (B).
\[ 5-3=2,\quad 7-5=2,\quad 9-7=2,\quad 11-9=2 \] Common difference is constant (=2).
Arithmetic sequence.
Step 3: Check Option (C).
\[ 4-2=2,\quad 8-4=4,\quad 16-8=8 \] Differences are not constant.
Not an arithmetic sequence.
Step 4: Check Option (D).
\[ 2-1=1,\quad 4-2=2,\quad 8-4=4 \] Differences are not constant.
Not an arithmetic sequence.
Hence, the correct answer is (B).
Step 1: Check Option (A).
\[ 4-1=3,\quad 9-4=5,\quad 16-9=7 \] Differences are not constant.
Not an arithmetic sequence.
Step 2: Check Option (B).
\[ 5-3=2,\quad 7-5=2,\quad 9-7=2,\quad 11-9=2 \] Common difference is constant (=2).
Arithmetic sequence.
Step 3: Check Option (C).
\[ 4-2=2,\quad 8-4=4,\quad 16-8=8 \] Differences are not constant.
Not an arithmetic sequence.
Step 4: Check Option (D).
\[ 2-1=1,\quad 4-2=2,\quad 8-4=4 \] Differences are not constant.
Not an arithmetic sequence.
Hence, the correct answer is (B).
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