Given:
In an arithmetic sequence,
![a_1=2](https://tex.z-dn.net/?f=a_1%3D2)
![a_i=a_{i-1}-3](https://tex.z-dn.net/?f=a_i%3Da_%7Bi-1%7D-3)
To find:
The sum of the first 335 terms in the given sequence.
Solution:
The recursive formula of an arithmetic sequence is:
...(i)
Where, d is the common difference.
We have,
...(ii)
On comparing (i) and (ii), we get
![d=-3](https://tex.z-dn.net/?f=d%3D-3)
The sum of first i terms of an arithmetic sequence is:
![S_i=\dfrac{i}{2}[2a+(i-1)d]](https://tex.z-dn.net/?f=S_i%3D%5Cdfrac%7Bi%7D%7B2%7D%5B2a%2B%28i-1%29d%5D)
Putting
, we get
![S_{335}=\dfrac{335}{2}[2(2)+(335-1)(-3)]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B2%282%29%2B%28335-1%29%28-3%29%5D)
![S_{335}=\dfrac{335}{2}[4+(334)(-3)]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B4%2B%28334%29%28-3%29%5D)
![S_{335}=\dfrac{335}{2}[4-1002]](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%5B4-1002%5D)
![S_{335}=\dfrac{335}{2}(-998)](https://tex.z-dn.net/?f=S_%7B335%7D%3D%5Cdfrac%7B335%7D%7B2%7D%28-998%29)
On further simplification, we get
![S_{335}=335\times (-499)](https://tex.z-dn.net/?f=S_%7B335%7D%3D335%5Ctimes%20%28-499%29)
![S_{335}=-167165](https://tex.z-dn.net/?f=S_%7B335%7D%3D-167165)
Therefore, the sum of the first 335 terms in the given sequence is -167165.
1 each hour 20-11=9 there is 9 hours between 11pm and 8:54am so 1 per each hour hope that it helped ;)
Analyze perfect cubes:
1^3 = 1
2^3 = 8
3^3 = 27
Since 12 is between 8 and 27, cube root of 12 is between 2 and 3.
You also know it is much closer to 2, since 12 is much closer to 8.
A good guess would be 2.25
(2.25)^3 = 11.39
This is close but slightly less than 12.
When you use your calculator you should get 2.2894.
Answer:
a = 28
b = 87
Step-by-step explanation:
By definition, opposite sides of a parallelogram are equal. So we can set the two expressions equal and solve for a:
a - 10 = 18
a = 28
Also by definition, opposite angles of a parallelogram are congruent. So set those two expressions equal and solve for b:
b + 16 = 103
b = 87
Hope this helps!
Answer: can somebody help me w my recent marking brainlist
Step-by-step explanation:
Sorry ik this isn’t the answer :(