arithmetic

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Questions and Answers

What is the common difference of the arithmetic sequence: 3, 7, 11, 15, ...?

  • 4 (correct)
  • 3
  • 2
  • 5

Find the next three terms of the arithmetic sequence: -2, 1, 4, 7, ...

  • 8, 9, 10
  • 9, 12, 15
  • 10, 13, 16 (correct)
  • 11, 14, 17

If the first term of an arithmetic sequence is 5 and the common difference is -3, what is the 6th term?

  • -13
  • -10 (correct)
  • 13
  • 10

Find the sum of the first 10 terms of the arithmetic sequence: 2, 5, 8, 11, ...

<p>155 (B)</p> Signup and view all the answers

The 5th term of an arithmetic sequence is 18 and the 10th term is 38. What is the common difference?

<p>4 (D)</p> Signup and view all the answers

Insert three arithmetic means between 2 and 26.

<p>8, 14, 20 (A)</p> Signup and view all the answers

The sum of the first and the last term of an arithmetic sequence is 40. If there are 8 terms in the sequence, find the sum of all the terms.

<p>160 (A)</p> Signup and view all the answers

In an arithmetic sequence, the 15th term is 55 and the 21st term is 85. Find the first term.

<p>5 (C)</p> Signup and view all the answers

In an arithmetic sequence, the 7th term is 34 and the 10th term is 49. Find the sum of the first 20 terms.

<p>820 (B)</p> Signup and view all the answers

Flashcards

Common Difference

The constant value added to each term in an arithmetic sequence.

Finding Next Terms

Add the common difference repeatedly to find subsequent terms.

Finding a Specific Term

Use the formula: a_n = a_1 + (n - 1) * d, where a_n is the nth term, a_1 is the first term, and d is the common difference.

Sum of First 'n' Terms

Use the formula: S_n = n/2 * [2a_1 + (n - 1) * d], where S_n is the sum of the first n terms.

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Finding Common Difference (Given Terms)

d = (a_n - a_m) / (n - m), if the nth term is a_n and the mth term is a_m.

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Arithmetic Means

Terms inserted between two given terms to form an arithmetic sequence.

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Sum of Arithmetic Sequence

Sum = (Number of terms / 2) * (First term + Last term)

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Finding First Term

Determine the common difference first, then work backwards to find the first term.

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Finding Common Difference

Determine the common difference from given terms and use the sum formula.

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Sum of First 20 Terms

Find the first term and common difference, then use the sum formula for the first 20 terms.

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