4 months ago
Q:

Which rule can you use to find the nth term of an arithmetic sequence in which the common difference is 5 and a12 = 63?

Accepted Solution

A:
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General formula :
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[tex]T_n = a_1 + d(n - 1)[/tex]

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Find [tex]a_1[/tex]:
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[tex]d = 5, a_{12}= 63,[/tex]

[tex]T_{12} = a_1 + 5(12 - 1)[/tex]

[tex]63= a_1 + 5(11)[/tex]

[tex]a_1 = 63 - 55[/tex]

[tex]a_1 = 8[/tex]

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Find equation for nth term :
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[tex]a_1 = 8, d = 5,[/tex]

[tex]T_n = 8 + 5(n-1)[/tex]

[tex]T_n = 8 + 5n - 5[/tex]

[tex]T_n = 5n + 3[/tex]

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[tex]\bf \text { Answer : }T_n = 5n + 3[/tex]
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