Answer:
The answer for the problem would be -12
Step-by-step explanation:
(28+35) = 63
63-75= -12
<u>Hint </u><u>:</u><u>-</u>
- Break the given sequence into two parts .
- Notice the terms at gap of one term beginning from the first term .They are like
. Next term is obtained by multiplying half to the previous term . - Notice the terms beginning from 2nd term ,
. Next term is obtained by adding 3 to the previous term .
<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>
We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,
.
We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,
Notice the term
will be too small , so we can neglect it and take its approximation as 0 .

Now the second sequence is in Arithmetic Progression , with common difference = 3 .
![\implies S_2=\dfrac{n}{2}[2a + (n-1)d]](https://tex.z-dn.net/?f=%5Cimplies%20S_2%3D%5Cdfrac%7Bn%7D%7B2%7D%5B2a%20%2B%20%28n-1%29d%5D%20)
Substitute ,
![\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}](https://tex.z-dn.net/?f=%5Cimplies%20S_2%3D%5Cdfrac%7B25%7D%7B2%7D%5B2%284%29%20%2B%20%2825-1%293%5D%20%3D%5Cboxed%7B%20908%7D%20)
Hence sum = 908 + 1 = 909
2w + 2l = 25
2 * 2 + 2l = 25
<em><u>Simplfiy.</u></em>
4 + 2l = 25
<em><u>Subtract 4 from both sides.</u></em>
2l = 21
<em><u>Divide both sides by 2.</u></em>
l = 10.5
Now that we have the value of l, we can find the area.
A = lw
A = 10.5 * 2
A = 21.
The length is 10.5cm.
The area of the rectangle is 21cm^2
Answer:
-6 = m (i'll show my work below)
Step-by-step explanation:
-6(m-7) + 7 = -8m + 37
-6m + 42 + 7 = -8m + 37
-6m + 49 = -8m +37
-37 = -37
-6m + 12 = -8m
+6m = +6m
12 = -2m
/-2 = /-2
-6 = m