Answer:
The sum of first five term of GP is 19607.
Step-by-step explanation:
We are given the following in the question:
A geometric progression with 7 as the first term and 7 as the common ration.
![a, ar, ar^2,...\\a = 7\\r = 7](https://tex.z-dn.net/?f=a%2C%20ar%2C%20ar%5E2%2C...%5C%5Ca%20%20%3D%207%5C%5Cr%20%3D%207)
![7, 7^2, 7^3, 7^4...](https://tex.z-dn.net/?f=7%2C%207%5E2%2C%207%5E3%2C%207%5E4...)
Sum of n terms in a geometric progression:
![S_n = \displaystyle\frac{a(r^n - 1)}{(r-1)}](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cdisplaystyle%5Cfrac%7Ba%28r%5En%20-%201%29%7D%7B%28r-1%29%7D)
For sum of five terms, we put n= 5, a = 7, r = 7
![S_5 = \displaystyle\frac{7(7^5 - 1)}{(7-1)}\\\\S_5 = 19607](https://tex.z-dn.net/?f=S_5%20%3D%20%5Cdisplaystyle%5Cfrac%7B7%287%5E5%20-%201%29%7D%7B%287-1%29%7D%5C%5C%5C%5CS_5%20%3D%2019607)
The sum of first five term of GP is 19607.
Verification:
![2801\times 7 = 19607](https://tex.z-dn.net/?f=2801%5Ctimes%207%20%3D%2019607)
Thus, the sum is equal to product of 2801 and 7.
Answer:
5381.6
Step-by-step explanation:
![(2.1 × 1016) + (3.2 × 1015)](https://tex.z-dn.net/?f=%282.1%20%C3%97%201016%29%20%2B%20%283.2%20%C3%97%201015%29)
![= 5381.6](https://tex.z-dn.net/?f=%20%3D%205381.6)
Answer: 11/18
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Explanation:
We need to add the fractions, but first we need to get each fraction to have the LCD (lowest common denominator) of 18
18 is the LCM of the denominators 6 and 9
The fraction 1/6 turns into 3/18 when multiplying top and bottom by 3
The fraction 4/9 turns into 8/18 after multiplying top and bottom by 2
Therefore,
(1/6) + (4/9) = (3/18) + (8/18) = (3+8)/18 = 11/18
So Mike has a total of 11/18 of a gallon of paint when combining the two given amounts 1/6 a gallon of blue paint and 4/9 of a gallon of green paint.