Mathematics: Don saves $1 the first week, 2$ the second week, $3 the third week, and $4 the fourth week. if he continues in this way, how many weeks will it take before don has saved at least $50? show me the simplest and quickest way to solve this problem. explain your steps

Don saves $1 the first week, 2$ the second week, $3

Ответ:

tbowlby7620

30.12.2021

This forms an arithmetic sequence, where the first term = 1, common difference = 1, and number of terms = n.

The formula for the sum of an arithmetic sequence is

$S_{n} = \frac{1}{2}n(2a + (n - 1)d)$

Where a = the first term and d = the common difference.

We want the sum to be at least $50, so
$50 \leq \frac{1}{2}n(2a + (n - 1)d)$

Substituting in a and d
$50 \leq \frac{1}{2}n(2(1) + (n - 1)(1))$

Rearranging
$50 \leq \frac{1}{2}n(2 + (n - 1))$
$50 \leq \frac{1}{2}n(1 + n)$
$100 \leq n(1 + n)$
$100 \leq n^2 + n$
$0 \leq n^2 + n - 100$

$\text{Let } n^2 + n -100 = 0$
$n = \frac{-1 \pm \sqrt{1-4(1)(-100)}}{2}$
$n = \frac{-1 \pm \sqrt{401}}{2}$
$n \geq 0 \implies n = \frac{-1 + \sqrt{401}}{2}$
$n \approx 9.51$

So it will take 9.51 weeks, or 10 weeks to the nearest week.

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Ответ:

Jasten

01.05.2022

Mathematics

Since 7-(-11) is in absolute value you have to change it to 7-11

In absolute value a positive is a positive and a negative is a positive.

When subtracting a smaller number from a bigger number you have to remember that it will always be negative. So just subtract 11 from 7 and add a negative sign.

11-7=4 so 7-11=-4.

If it wasn't in absolute value it would be different.

I hope that helps!

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Don saves $1 the first week, 2$ the second week, $3 the third week, and $4 the fourth week. if he continues in this way, how many weeks will it take before don has saved at least $50?
show me the simplest and quickest way to solve this problem. explain your steps

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