<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
<u>1/3; 2/7; 2/9</u>
Lets find least common multiple
The least common multiple is 63
1/3 --> 21/63
2/7 --> 18/63
2/9 --> 14/63
As you can see I am correct, but I found the LCM by multiplying 1/3 by 21 to get to 63 and the numerator as well
Answer:
2t-7
Step-by-step explanation:
Not sure what you need ;( hope this helps!
11 and 12.
the square of 11 is 121 and the square of 12 is 144 and because 140 is between 121 and 144, 11 and 12 are the correct answer.
