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3 years ago

What is the explicit formula for this sequence? -7,-3,1,5

Mathematics

1 answer:

uranmaximum [27]3 years ago

6 0

Answer:

$a_{n}$ = 4n - 11

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

d = - 3 - (- 7) = 1 - (- 3) = 5 - 1 = 4

and a₁ = - 7, hence

$a_{n}$ = - 7 + 4(n - 1) = - 7 + 4n - 4 = 4n - 11

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Answer:

(a)

$\begin{array}{ccc}{} & {W} & {w} & {w} & {Ww } & {ww } & {w} & { Ww} & {ww } \ \end{array}$

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Step-by-step explanation:

See attachment for initial punnet square

Solving (a): Complete the square

Initially, we have:

$\begin{array}{ccc}{} & {W} & {w} & {w} & { } & { } & {w} & { } & { } \ \end{array}$

To complete the square, we simply write the letter at the column and the letter at the row in each cell;

So, we have:

$\begin{array}{ccc}{} & {W} & {w} & {w} & {Ww } & {ww } & {w} & { Ww} & {ww } \ \end{array}$

Solving (b): Percentage of each

From the question, we understand that W are dominant to w.

So:

$Ww = White$

$ww = Yellow$

From (a) above

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$ww = 2$

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So, the percentage of each is:

$White = \frac{Ww}{Total} * 100\%$

$White = \frac{2}{4} * 100\%$

$White = 0.5 * 100\%$

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$Yellow = 100\% - White$ --- Complement rule

$Yellow = 100\% - 50\%$

$Yellow = 50\%$

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