-13 is the smallest among these integers.
Answer:
(a)= option 3
(b)= option 3
Step-by-step explanation:
(A) It is given that a sequence is defined by the recursive function
and ![a_{n}=a_{n-1}+n](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Bn)
Now, substituting the value of n=2 in above equation,
![a_{2}=a_{1}+2](https://tex.z-dn.net/?f=a_%7B2%7D%3Da_%7B1%7D%2B2)
![a_{2}=1+2](https://tex.z-dn.net/?f=a_%7B2%7D%3D1%2B2)
![a_{2}=3](https://tex.z-dn.net/?f=a_%7B2%7D%3D3)
Again putting n=3,
![a_{3}=a_{2}+3](https://tex.z-dn.net/?f=a_%7B3%7D%3Da_%7B2%7D%2B3)
![a_{3}=3+3](https://tex.z-dn.net/?f=a_%7B3%7D%3D3%2B3)
![a_{2}=6](https://tex.z-dn.net/?f=a_%7B2%7D%3D6)
Putting n=4,
![a_{4}=a_{3}+4](https://tex.z-dn.net/?f=a_%7B4%7D%3Da_%7B3%7D%2B4)
![a_{4}=6+4](https://tex.z-dn.net/?f=a_%7B4%7D%3D6%2B4)
![a_{4}=10](https://tex.z-dn.net/?f=a_%7B4%7D%3D10)
Putting n=5,
![a_{5}=a_{4}+5](https://tex.z-dn.net/?f=a_%7B5%7D%3Da_%7B4%7D%2B5)
![a_{5}=10+5](https://tex.z-dn.net/?f=a_%7B5%7D%3D10%2B5)
![a_{5}=15](https://tex.z-dn.net/?f=a_%7B5%7D%3D15)
Putting n=6,
![a_{6}=a_{5}+6](https://tex.z-dn.net/?f=a_%7B6%7D%3Da_%7B5%7D%2B6)
![a_{6}=15+6](https://tex.z-dn.net/?f=a_%7B6%7D%3D15%2B6)
![a_{6}=21](https://tex.z-dn.net/?f=a_%7B6%7D%3D21)
Putting n=7,
![a_{7}=a_{6}+7](https://tex.z-dn.net/?f=a_%7B7%7D%3Da_%7B6%7D%2B7)
![a_{7}=21+7](https://tex.z-dn.net/?f=a_%7B7%7D%3D21%2B7)
![a_{7}=28](https://tex.z-dn.net/?f=a_%7B7%7D%3D28)
Hence, option 3 is correct.
(B) The given sequence is :
5, -10, 20, -40, 80.....
Since, the given sequence is GP, therefore
and r=-2
The nth term is given by:
![a_{n}=a_{1}r^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7B1%7Dr%5E%7Bn-1%7D)
For fifteenth term, put n=15 in above equation, we get
![a_{15}=5(-2)^{14}](https://tex.z-dn.net/?f=a_%7B15%7D%3D5%28-2%29%5E%7B14%7D)
=![5{\times}16384](https://tex.z-dn.net/?f=5%7B%5Ctimes%7D16384)
=![81920](https://tex.z-dn.net/?f=81920)
Hence, the fifteenth term is 81920.
Option 3 is correct.
Answer:
1.3455
Step-by-step explanation:
A 15% increase is a multiplication by 1.15
So a 15% and a 17% increase is a multiplication of 1.15*1.17 = 1.3455
8/12: 2/3 and 16/24
6/8: 3/4 and 12/16
9/15: 3/5 and 18/30
2/16: 1/8 and 4/32
Answer:
a+b = 4![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
Step-by-step explanation:
3(a + b)^2 = 81
(a + b)^2 = 27
a + b = sq rt 27
a + b =
· ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
a + b = 3![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)