Find the number of terms in an AP given that it's first and last term are a and 37a respectively and that it's common difference is 4a
Let the number of terms in the arithmetic progression be n. The first term is a and the last term is 37a. The common difference is 4a.
We know that the nth term of an arithmetic progression is given by:
T_n = a + (n - 1)d
Substituting in the values, we have:
37a = a + (n - 1)(4a)
Simplifying the equation, we get:
37a = a + 4an - 4a
Combining like terms, we have:
37a = a(4n - 3)
Dividing both sides by (4n - 3), we get:
37a / (4n - 3) = a
Cancelling out the "a" terms, we have:
37 / (4n - 3) = 1
Simplifying the equation, we get:
37 = 4n - 3
Adding 3 to both sides, we have:
40 = 4n
Dividing both sides by 4, we get:
n = 10
Therefore, the number of terms in the arithmetic progression is 10.
To find the number of terms in an arithmetic progression (AP), you can use the formula:
n = (last term - first term) / common difference + 1
Given that the first term is "a", the last term is "37a", and the common difference is "4a", we can substitute these values into the formula:
n = (37a - a) / (4a) + 1
Simplifying, we have:
n = 36a / 4a + 1
n = 9 + 1
n = 10
Therefore, the number of terms in the arithmetic progression is 10.
To find the number of terms in an arithmetic progression (AP), you need to know the first term (a), the common difference (d), and the last term (l). In the given problem, the first term (a) is provided as well as the last term (37a). The common difference (4a) is also given.
To find the number of terms, you can use the formula for the nth term of an AP:
l = a + (n-1)d
Here, l represents the last term, a is the first term, n is the number of terms, and d is the common difference.
We can substitute the given values into the formula and solve for n:
37a = a + (n - 1)(4a)
Now, let's simplify the equation:
37a = a + 4an - 4a
Combine like terms:
37a = a - 3a + 4an
Remove the common factor of 'a' from both sides:
37 = 1 - 3 + 4n
Combine like terms:
37 = -2 + 4n
Add 2 to both sides:
39 = 4n
Divide both sides by 4:
n = 39/4
So, the number of terms in the arithmetic progression is 39/4. However, this is not a whole number, which suggests that the number of terms may not be an exact integer.
If you prefer a whole number answer, you can round the result up or down depending on your requirements.