Answer :
1) the sum of the numbers from 7 to 89 using Gauss's Method is 4032. 2) the sum of the sequence 1, 5, 25, 125, 625, 3125 using Euclid's Method is 3906.
How to Use Gauss's Method to sum the numbers
1. Gauss's Method can be used to sum a sequence of numbers by finding the average of the first and last terms and multiplying it by the number of terms. In this case, we have a sequence from 7 to 89.
The first term, a = 7
The last term, b = 89
The number of terms, n = (b - a) + 1 = (89 - 7) + 1 = 83 + 1 = 84
The sum of the sequence can be calculated as:
Sum = (n/2) * (a + b)
= (84/2) * (7 + 89)
= 42 * 96
= 4032
Therefore, the sum of the numbers from 7 to 89 using Gauss's Method is 4032.
2. Euclid's Method is used to find the sum of a geometric sequence. In this case, we have the sequence 1, 5, 25, 125, 625, 3125.
To find the sum of this sequence, we can use the formula:
Sum =[tex]a * (r^n - 1) / (r - 1)[/tex]
Here, a = 1 (the first term)
r = 5 (the common ratio)
n = 6 (the number of terms)
Using these values, we can calculate the sum as follows:
Sum = [tex]1 * (5^6 - 1) / (5 - 1)[/tex]
= 1 * (15625 - 1) / 4
= 15624 / 4
= 3906
Therefore, the sum of the sequence 1, 5, 25, 125, 625, 3125 using Euclid's Method is 3906.
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