<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 ,
![\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]](https://tex.z-dn.net/?f=%5Cimplies%20S_1%20%3D%20a%5Cdfrac%7B1-r%5En%7D%7B1-r%7D%20%5C%5C%5C%5C%5Cimplies%20S_1%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Cleft%5B%20%5Cdfrac%7B1-%5Cbigg%28%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%29%5E%7B25%7D%7D%7B1-%5Cdfrac%7B1%7D%7B2%7D%7D%5Cright%5D%20)
Notice the term 
will be too small , so we can neglect it and take its approximation as 0 .
![\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]](https://tex.z-dn.net/?f=%5Cimplies%20S_1%5Capprox%20%5Ccancel%7B%20%5Cdfrac%7B1%7D%7B2%7D%20%7D%20%5Cleft%5B%20%5Cdfrac%7B1-0%7D%7B%5Ccancel%7B%5Cdfrac%7B1%7D%7B2%7D%20%7D%7D%5Cright%5D%20)
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
Hello from MrBillDoesMath!
Answer: infinite solutions
Discussion: I did a double take on this one but the left hand is
a + 3 + 2a = 3a +3
and the right hand side is
-1 + 3a + 4 = 3a + (4-1) = 3a + 3
The left and right sides of the equation are identical for all "a", i.e. for infinitely many "a" values.
Regards, MrB.
Distribute 3
6t+15=5t+25
subtract 5t from 6t
t+15=25
subtract 15 from both sides
t=10
Answer:
The answer is 24
Step-by-step explanation:
Answer: The table represents a function. What is f(5)?
–8
–1
1
8
Step-by-step explanation:
