The first term of an AP is s and d=-3/2, find the term whose value is -201/2.
solve for n:
s + (n-1)(-3/2) = -201/2
Why did the terms of the AP go on a diet? Because they wanted to be minus-size! Now, let's solve the problem.
In an arithmetic progression (AP), we can use the formula for the nth term to find the term we're looking for. The formula is:
tn = a + (n-1)d
Where:
tn is the nth term,
a is the first term,
n is the term number, and
d is the common difference.
Given that the first term (a) is s and the common difference (d) is -3/2, we can substitute these values into the formula:
tn = s + (n-1)(-3/2)
Now, setting tn to -201/2, we have:
-201/2 = s + (n-1)(-3/2)
To avoid any further diet jokes, let's solve this equation!
To find the term whose value is -201/2 in an arithmetic progression (AP) with a first term, s, and a common difference, d=-3/2, we can use the formula for the nth term of an AP:
a_n = a_1 + (n-1)d
We are given that the first term, a_1, is s, and we need to find the value of n for which a_n is -201/2.
Setting the value of a_n to -201/2, we have:
-201/2 = s + (n-1)(-3/2)
Multiplying both sides by 2 to eliminate the fraction:
-201 = 2s - 3(n-1)
Expanding the brackets:
-201 = 2s - 3n + 3
Rearranging the equation:
2s - 3n = -204
Now, we need to solve this equation for n. Since we don't have the value of s, we'll leave the equation in terms of s and n.
If you have the value of s, substitute it into this equation and solve for n.
To find the term in an arithmetic progression (AP), we need to use the formula for the n-th term of an AP:
a_n = a_1 + (n - 1) * d,
where:
- a_n is the n-th term,
- a_1 is the first term,
- n is the position of the term in the sequence, and
- d is the common difference between the terms.
In this case, we are given that the first term of the AP is s and d = -3/2. We want to find the term whose value is -201/2.
Let's substitute the given values into the formula:
-201/2 = s + (n - 1) * (-3/2).
To solve for n, let's rearrange the equation:
-3n/2 + 201/2 = s.
Next, let's solve for n by getting it on one side of the equation:
-3n/2 = s - 201/2.
Multiply both sides of the equation by -2/3 to isolate n:
n = (s - 201/2) * (-2/3).
Now we have an expression to find n, given s. Plug in the value of s to get n.
It's important to note that the value of s is not given in the question. If you have a value for s, you can substitute that in the expression above to find n.