Write down the next three terms in these arithmetic sequences
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Write down the next three terms in these arithmetic sequences
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Find the sum of the first four terms in the sequence defined by .
Justify why this sequence is an arithmetic sequence.
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Write down a formula for the th term of each of the following arithmetic sequences
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Find the 10th and 20th terms in each of the following arithmetic sequences
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The 4th and 8th terms of an arithmetic sequence are 20 and 64 respectively.
Find the first term and the common difference.
The 12th and 16th terms of an arithmetic sequence differ by 20.
Find the possible values of the common difference.
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Find the sum of the first 20 terms of the arithmetic series that has first term 3 and common difference 4.
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The first term of an arithmetic sequence is 3.
The 10th term of the sequence is 30.
The sum of the first terms is 630.
Find the common difference.
Show that .
Hence find the value of .
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An arithmetic series is given by
where is a constant.
Write down a formula for the th term of the series, in terms of .
Show that the sum of the first terms is .
The sum of the first 12 terms is 39.
Find the value of .
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The first three terms in an arithmetic sequence are
Find the value of .
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The first three terms in an arithmetic sequence are
Find the possible values of .
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An arithmetic sequence has first term and common difference , where . The fifth term of the sequence is 85.
Find:
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The third term of an arithmetic series is 2. The twelfth term is 65. The sum of the first terms is 390.
Show that .
Hence find the value of .
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The sum of the first ten terms in an arithmetic series is 40. The sum of the first twenty terms in the same series is 280. Find the first term, , and the common difference, , of the series.
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The sum of the first terms of an arithmetic series is
Show that .
Hence show that the sum of the first terms is .
Given that , find the value of .
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The fifth term of an arithmetic series is , where is a constant, and the sum of the first eight terms of the series is .
Show that the first term, , of the series is .
Find an expression for the common difference, , of the series in terms of .
Given that the ninth term of the sequence is 14, calculate:
the value of
The sum of the first 30 terms of the series.
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Calculate the sum of all the odd numbers between 0 and 150,
An arithmetic series is defined by
where is an integer and a positive factor of 360.
In terms of , find the 100th term of the arithmetic sequence defined by
Give your answer in simplest form.
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The first three terms in an arithmetic sequence are
Find the possible values of .
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The first two terms in an arithmetic sequence are and 3. The fourth term is .
Find the value of .
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An arithmetic sequence has first term and common difference , where . The fourth term in the sequence is 4.
Find the value of , giving your answer as an exact value.
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The third term of an arithmetic series is 32. The eleventh term is 0. The sum of the first terms is -44.
Find the value of .
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The sum of the first twelve terms in an arithmetic series is 654. The sum of the first twenty terms in the same series is 530. Find the 21st term.
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Prove that the sum of the first odd numbers is a square number for any value of .
An arithmetic series is defined by
where is an integer.
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The seventh term of an arithmetic series is , where is a constant, and the sum of the first nine terms of the series is .
In terms of , find expressions for the first term and common difference of the series.
Given that the nineteenth term of the sequence is 57, find the sum of the first 25 terms of the series.
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An arithmetic series is defined by
Find an expression for in terms of and
For a particular value of , and .
Find the value of .
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The first four terms in an arithmetic sequence are
Find the values of and .
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The first three terms in an arithmetic sequence are
Given that the first three terms in the sequence are all positive, find the fortieth term in the sequence.
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An arithmetic sequence has first term and common difference , where . The ninth term in the sequence is 7.
is the set of all numbers that are in the sequence. is the set of all rational numbers.
Determine the elements of the set .
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The th term of an arithmetic series is 0. The sum of the first terms is also 0.
Find the value of in terms of , giving clear reasons for your answer.
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The sum of the first 20 terms in an arithmetic series is 290. The sum of the first 24 terms in the same series is -180. In general, the sum of the first terms is . Find the greatest value attained by for any
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The sum of the first 24 terms in an arithmetic series is nine times the sum of the first two terms in the series.
Find the sum of the first 90 terms in the series.
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The th term in an arithmetic sequence can be expressed in the form
In 4
Show that the sum of the first terms of the sequence is
In 2
where is a polynomial in to be found.
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An arithmetic sequence is defined by
Find, in terms of and , an expression for the sum of the first terms of the sequence.
Hence find the smallest value of for which the sum of the first terms of the sequence is greater than zero.
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