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2 years ago

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Find an equation for the nth term of the arithmetic sequence. -15, -6, 3, 12, ...

1 answer:

Mariulka [41]2 years ago

5 0

Answer: $t_{n}=-15+9(n-1)$

Step-by-step explanation:

The formula for finding the nth term of an arithmetic sequence is given as:

$t_{n}=a+(n-1)d$

$a =$ first term = -15

$d =$ common difference = -6 - (-15) = 9

$n =$ number of terms

substituting into the formula , we have :

$t_{n} = -15+(n-1)9$

$t_{n}=-15+9(n-1)$

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cestrela7 [59]

Step $1$

<u>Find the irreducible fraction in each ratio</u>

<u>case 1)</u> $\frac{40}{64}$

Divide by $8$ boths numerator and denominator

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<u>case 2)</u> $\frac{5}{75}$

Divide by $5$ boths numerator and denominator

$\frac{5}{75}=\frac{1}{15}$

<u>case 3)</u> $\frac{14}{35}$

Divide by $7$ boths numerator and denominator

$\frac{14}{35}=\frac{2}{5}$

<u>case 4)</u> $\frac{24}{64}$

Divide by $8$ boths numerator and denominator

$\frac{24}{64}=\frac{3}{8}$

<u>case 5)</u> $\frac{6}{15}$

Divide by $3$ boths numerator and denominator

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<u>case 6)</u> $\frac{65}{104}$

Divide by $13$ boths numerator and denominator

$\frac{65}{104}=\frac{5}{8}$

<u>case 7)</u> $\frac{66}{176}$

Divide by $22$ boths numerator and denominator

$\frac{66}{176}=\frac{3}{8}$

<u>case 8)</u> $\frac{12}{30}$

Divide by $6$ boths numerator and denominator

$\frac{12}{30}=\frac{2}{5}$

<u>case 9)</u> $\frac{15}{225}$

Divide by $15$ boths numerator and denominator

$\frac{15}{225}=\frac{1}{15}$

<u>case 10)</u> $\frac{6}{16}$

Divide by $2$ boths numerator and denominator

$\frac{6}{16}=\frac{3}{8}$

<u>case 11)</u> $\frac{15}{24}$

Divide by $3$ boths numerator and denominator

$\frac{15}{24}=\frac{5}{8}$

<u>case 12)</u> $\frac{48}{128}$

Divide by $16$ boths numerator and denominator

$\frac{48}{128}=\frac{3}{8}$

Step $2$

<u>Sort the ratios into bins</u>

1<u>) First Bin</u>

<u> $Ratio=\frac{5}{8}$ </u>

$\frac{40}{64}$

$\frac{65}{104}$

$\frac{15}{24}$

<u>2) Second Bin </u>

<u> $Ratio=\frac{1}{15}$ </u>

$\frac{5}{75}$

$\frac{15}{225}$

<u>3) Third Bin</u>

$Ratio=\frac{2}{5}$

$\frac{14}{35}$

$\frac{6}{15}$

$\frac{12}{30}$

4<u>) Fourth Bin</u>

<u> $Ratio=\frac{3}{8}$ </u>

$\frac{24}{64}$

$\frac{66}{176}$

$\frac{6}{16}$

$\frac{48}{128}$

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