What number can be added to -2 to get a sum of 0?

The third through the fifth terms of a geometric sequence are given by a3 = 18, a4 = 27 , and a5 = 81/2

Kaylis [27]

Let a be the first term in the sequence. If r is the ratio between consecutive terms, then the second term is ar, the third term is ar ^2, the fourth is ar ^3, and so on, up to the n-th term ar ^(n - 1).

So the third, fourth, and fifth terms are such that

ar ^2 = 18

ar ^3 = 27

ar ^4 = 81/2

Solve for a and r :

(ar ^3) / (ar ^2) = 27/18 => r = 3/2

ar ^2 = a (3/2)^2 = 9/4 a = 18 => a = 8

Then the n-th term in the sequence is

ar ^(n - 1) = 9 (3/2)^(n - 1)

You can rewrite this by first rewriting 9 = 3^2, then

9 (3/2)^(n - 1) = 3^2 * 3^(n - 1) / 2^(n - 1) = 3^(n + 1)/2^(n - 1)

6 0

3 years ago

Math help? Easy but I can't get it! :(

Vladimir79 [104]

Ok, so, the question states that the distance driven is proportional to the time driven in hours. So, the x value would be hours driven, while the y-value would be the number of miles driven. So, in order to find the speed at which she is driving, you will want to divide the number of miles by the number of hours driving, or 180/3, You answer should be 60, or 60 mph is her speed.

4 0

3 years ago

Read 2 more answers

A running circuit is in the shape of a triangle with lengths of 6km, 6.5km and 7km. What are the sizes of the angles (in minutes

Rudik [331]

A triangle is an example of a class of figures referred to as plane shapes. It has three straight sides and three internal angles which sum up to $180^{o}$ . The measures of the internal angles of the triangle given in the question are A = $52.6^{o}$ , B = $59.4^{o}$ , and C = $68^{o}$ .

A triangle is an example of a class of figures referred to as plane shapes. It has three straight sides and three internal angles which sum up to $180^{o}$ .

Considering the given question, let the sides of the triangle be: a = 6 km, b = 6.5 km, and c = 7 km.

Apply the Cosine rule to have:

$c^{2}$ = $a^{2}$ + $b^{2}$ - 2ab Cos C