Question

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

Answer 1

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General formula :
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$T_n = a_1 + d(n - 1)$

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Find $a_1$:
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$d = 5, a_{12}= 63,$

$T_{12} = a_1 + 5(12 - 1)$

$63= a_1 + 5(11)$

$a_1 = 63 - 55$

$a_1 = 8$

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Find equation for nth term :
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$a_1 = 8, d = 5,$

$T_n = 8 + 5(n-1)$

$T_n = 8 + 5n - 5$

$T_n = 5n + 3$

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$\bf \text { Answer : }T_n = 5n + 3$
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