Solve for the 101st term of the sequence whose 1st term is x-y and d=2x+y-3.
a = x-y
d = 2x+y-3
just use your formula
term(101) = a + 100d
= x-y + 100(2x+y-3)
= x-y + 200x + 100y - 300
= 201x + 99y - 300
uwu
bruh
To solve for the 101st term of the given sequence, we first need to determine the general formula for the nth term of the sequence.
The given sequence has a first term (1st term) of x-y and a common difference (d) of 2x+y-3.
The general formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d
In this formula, an represents the nth term, a1 represents the first term, n represents the position of the term, and d represents the common difference.
Now, let's substitute the given values into the formula:
a1 = x - y
d = 2x + y - 3
Therefore, the general formula for the nth term of the sequence is:
an = (x - y) + (n - 1)(2x + y - 3)
Now, to find the value of the 101st term (a101), we substitute n = 101 into the general formula:
a101 = (x - y) + (101 - 1)(2x + y - 3)
Simplifying further, we have:
a101 = (x - y) + 100(2x + y - 3)
By expanding the brackets, we get:
a101 = (x - y) + 200x + 100y - 300
Combining like terms, we get:
a101 = 201x + 99y - 300
Thus, the 101st term of the sequence is given by the expression 201x + 99y - 300.