Please help me one this someone please!!!

Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first three terms is 26.

Serga [27]

Answer:

<h3>The nth term Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequences</h3>

Step-by-step explanation:

Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.

If the sum of the first two term is 24, then a/r + a = 24...(1)

and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)

Substtituting equation 1 into 2 we have;

24+ar = 26

ar = 2

a = 2/r ...(3)

Substituting a = 2/r into equation 1 will give;

(2/r))/r+2/r = 24

2/r²+2/r = 24

(2+2r)/r² = 24

2+2r = 24r²

1+r = 12r²

12r²-r-1 = 0

12r²-4r+3r -1 = 0

4r(3r-1)+1(3r-1) = 0

(4r+1)(3r-1) = 0

r = -1/4 0r 1/3

Since a= 2/r then a = 2/(-1/4)or a = 2/(1/3)

a = -8 or 6

All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of a geometric sequence is expressed as

if r = -1/4 and a = -8

Tn = -8(-1/4)^(n-1)

if r = 1/3 and a = 6

Tn = 6(1/3)^(n-1)

The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms

6 0

3 years ago

What is the value of x? and how did you do it

Nana76 [90]

Answer:

x = 45

Step-by-step explanation:

These angles equal to each other. So...

2x + 6 = 96

2x = 90

x = 45

I hope this helps :)

4 0

2 years ago

Read 2 more answers

HELP!!!!!!!!!!!!!!!!!!!!!!!!!! Can U Answer All These.

mash [69]

<u>QUESTION 1</u>

In figure A, the area of the bigger square is $625\:units^2$ . This means that the length of this square is the hypotenuse of the right angle triangle formed, which is $25\:units$ .

The area of the two smaller squares are $576\:units^2$ and $49\:units^2$ .

The length of these two squares form the two shorter legs of the right angle triangle, which are $24$ and $7$ units respectively.

Therefore we can write the equation, $576+49=625$ .

This implies that, $24^2+7^2=25^2$

We can see that the sum of the squares of the two shorter legs equals the square of the longer side which is the hypotenuse and this what the Pythagoras theorem says.

But in fig. B,

$5^2+4^2\ne 6^2$