give the sequence of 5 term if the first term is 8 and the last term is 100
there are 4 terms past the first, so divide 92/4 to get the difference between terms
To find the sequence of 5 terms with the first term being 8 and the last term being 100, you need to determine the common difference between consecutive terms.
Since you have 5 terms, the sequence can be represented as follows: 8, x, y, z, 100.
To find the common difference, subtract the first term from the second term: x - 8 = d.
Similarly, y - x = d, z - y = d, and 100 - z = d.
Since the common difference is the same for all pairs, you can set up the following equations:
x - 8 = y - x
y - x = z - y
z - y = 100 - z
By solving these equations simultaneously, you can find the values of x, y, and z. Here's how:
1. Start with the equation x - 8 = y - x.
Rearrange it to get: 2x = y + 8.
2. Substitute 2x for y in the equation y - x = z - y.
You then have: y - x = z - 2x.
Rearrange it to get: 3x = z - y.
3. Substitute z - y for 3x in the equation z - y = 100 - z.
You then have: z - y = 100 - (z - y).
Simplify it to get: z - y = 100 - z + y.
Rearrange it to get: 2z = 100 + 2y.
4. Substitute y + 8 for 2z in the equation 2z = 100 + 2y.
You then have: 2(y + 8) = 100 + 2y.
Simplify it to get: 2y + 16 = 100 + 2y.
Rearrange it to get: 16 = 100, which is false.
Since the equation is false, it means that there is no solution for the given conditions. Please double-check the information provided or let me know if you have any additional details.