Write the explicit formula for the geometric sequence. a1 = -5 a2 = 20 a3 = -80

1 answer:

6 0

$a_1 = -5;\ a_2 = 20;\ a_3 = -80 \\\\a_2:a_1=r\ and\ a_3:a_2=r\\\\r=20:(-5)=-4\ check\ r=-80:20=-4\\\\a_n=a_1r^{n-1}\to a_n=-5\cdot(-4)^{n-1}=-5\cdot(-4)^{-1}\cdot(-4)^n\\\\=-5\cdot\left(-\dfrac{1}{4}\right)\cdot(-4)^n=\dfrac{5}{4}\cdot(-4)^n\\\\Answer:\boxed{a_n=-5\cdot(-4)^{n-1}\ other\ a_n=\frac{5}{4}\cdot(-4)^n}$

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Find the first term and common difference of an AP, whose 7th term is 29/6 and 15th term is 11/2.

777dan777 [17]

Answer:

The first term is 13/3 and the common difference is d = 1/12

The formula is a(n) = 13/3 + (1/12)(n - 1)

Step-by-step explanation:

The general equation for an arithmetic progression is:

a(n) = a(1) + d(n - 1), where d is the common difference/

Case 1: n = 7: 29/6 = a(1) + d(7 - 1), or 29/6 = a(1) + d(6)

Case 2: n = 15: 11/2 = a(1) + d(15 - 1) = a(1) + d(14)

Then our system of linear equations is:

a(1) + 6d = 29/6

a(1) + 14d = 11/2

Let's solve this by elimination by addition and subtraction. Subtract the first equation from the second. We get:

Substituting 1/12 for d in the first equation, we get:

a(1) + 14(1/12) = 11/2 or 66/12 (using the LCD 12)

Then a(1) = 66/12 - 14/12 = 52/12 = 13/3

The first term is 13/3 and the common difference is d = 1/12

The arithmetic sequence formula for this problem is thus:

a(n) = 13/3 + (1/12)(n - 1) 8

5 0

3 years ago

What is slope when talking about math

dolphi86 [110]

When graphing, its how much you rise and run
thats the formula when u have a graph and the question is asking for the slope.
you chose a point, and go down or up however many times it goes to the next point, and you run to the left however many times it gets you to get to that point.
if the line goes downward the slope is therefore negative, and if the line goes upward, the slope is therefore, positive.
m in math is meant to be slope, so $m= \frac{rise}{run}$