How do you write a rule for the nth term of the arithmetic sequence $a_{6} = 43, a_{15} = 107.8$ $a_6=43, a_15=107.8$ ?

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How do you write a rule for the nth term of the arithmetic sequence $a_{6} = 43, a_{15} = 107.8$ $a_6=43, a_15=107.8$ ?

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Answer 1 · 2017-06-26T20:18:48

$a_{n} = 7.2 n - 0.2$ $a_n=7.2n-0.2$

Explanation:

$the nth term formula for an arithmetic sequence is$ $"the nth term formula for an arithmetic sequence is"$

$∙ a_{n} = a_{1} + (n - 1) d$ $• a_n=a_1+(n-1)d$

$where a_{1} is the first term and d the common difference$ $"where " a_1" is the first term and d the common difference"$

$a_{1} and d require to be found$ $a_1" and d require to be found"$

$using the nth term formula$ $"using the "color(blue)"nth term formula"$

$a_{6} = a_{1} + 5 d = 43 \to (1)$ $a_6=a_1+5d=43 to(1)$

$a_{15} = a_{1} + 14 d = 107.8 \to (2)$ $a_(15)=a_1+14d =107.8to(2)$

$(2) - (1)$ $(2)-(1)$

$\Rightarrow 9 d = 64.8$ $rArr9d=64.8$

$\Rightarrow d = 7.2$ $rArrd=7.2$

$substitute this value in (1) and solve for a_{1}$ $"substitute this value in " (1)" and solve for " a_1$

$a_{1} = 43 - (5 \times 7.2) = 7$ $a_1=43-(5xx7.2)=7$

$\Rightarrow a_{n} = 7 + (n - 1) 7.2$ $rArra_n=7+(n-1)7.2$

$\Rightarrow a_{n} = 7.2 n - 0.2$ $rArra_n=7.2n-0.2$

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How do you write a rule for the nth term of the arithmetic sequence $a_{6} = 43, a_{15} = 107.8$ $a_6=43, a_15=107.8$ ?

1 Answer

Explanation:

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How do you write a rule for the nth term of the arithmetic sequence a6=43,a15=107.8a_6=43, a_15=107.8?

1 Answer

Explanation:

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How do you write a rule for the nth term of the arithmetic sequence $a_{6} = 43, a_{15} = 107.8$ $a_6=43, a_15=107.8$ ?