Comprehension
5, 11, 17, .... is an arithmetic sequence.
Question: 1

Write the algebraic form of this sequence.

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A quick way to find the algebraic form: the common difference (6) is the coefficient of n. So the form is 6n + c. To find c, use the first term. For n=1, 6(1) + c = 5 c = -1. So the formula is 6n-1.
Updated On: Mar 16, 2026
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Question: 2

Calculate the sum of first 15 terms of this sequence.

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To multiply 15 × 47, you can do 15 × (50 - 3) = 750 - 45 = 705, which can be faster than traditional multiplication.
Updated On: Mar 16, 2026
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Question: 3

Write the sum of first n terms of this sequence.

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The sum of an arithmetic sequence, Sₙ, will always be a quadratic expression in n with no constant term. The coefficient of the n² term is always half the common difference (d/2). Here, d=6, so the term is (6/2)n² = 3n², which is a good way to check your result.
Updated On: Mar 16, 2026
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