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Given arithmetic sequences with some terms missing, fill in the missing terms.

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Fill in the gaps in the following arithmetic sequences.

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\$\\var{m[0]*(index[0])}, \\; \\var{m[0]*(index[0]+1)}, \\; \\var{m[0]*(index[0]+2)}, \\;\$ [[0]] \$, \\; \\var{m[0]*(index[0]+4)}, \\;\$ [[1]]\$, \\; \\var{m[0]*(index[0]+6)}\$

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\$\\var{m[1]*(index[1])}, \\; \\var{m[1]*(index[1]-1)}, \\;\$ [[0]]\$, \\; \\var{m[1]*(index[1]-3)}, \\; \\var{m[1]*(index[1]-4)}, \\;\$ [[1]] \$, \\; \\var{m[1]*(index[1]-6)}\$

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Starting indices of the sequences.

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Common differences of the sequences

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In an arithmetic sequence, the difference between two adjecent terms is always the same.

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#### a)

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The difference between the first two terms in this sequence is \$\\var{m[0]*(index[0]+1)} - \\var{m[0]*(index[0])} = \\var{m[0]}\$.

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So to get from one term to the next, add \$\\var{m[0]}\$.

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The complete sequence is

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\\[ \\var{m[0]*(index[0])}, \\; \\var{m[0]*(index[0]+1)}, \\; \\var{m[0]*(index[0]+2)}, \\; \\underline{\\var{m[0]*(index[0]+3)}}, \\; \\var{m[0]*(index[0]+4)}, \\; \\underline{\\var{m[0]*(index[0]+5)}}, \\; \\var{m[0]*(index[0]+6)} \\]

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#### b)

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The difference between the first two terms in this sequence is \$\\var{m[1]*(index[1]-1)} - \\var{m[1]*(index[1])} = \\var{-m[1]}\$.

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So to get from one term to the next, subtract \$\\var{m[1]}\$.

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The complete sequence is

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\\[ \\var{m[1]*(index[1])}, \\; \\var{m[1]*(index[1]-1)}, \\; \\underline{\\var{m[1]*(index[1]-2)}}, \\; \\var{m[1]*(index[1]-3)}, \\; \\var{m[1]*(index[1]-4)}, \\; \\underline{\\var{m[1]*(index[1]-5)}}, \\; \\var{m[1]*(index[1]-6)} \\]

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\n", "name": "Fill in the gaps in an arithmetic sequence", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}