if the first term of an AP is 3 and the last term is 48 find the number of terms in the AP if the sum of its term is 34?
sum of terms less than last term? Interesting.
simple. There are only 4/3 terms
n/2 (3+48) = 34
The sum of 2 terms is 51, so you clearly have fewer than 2 terms.
To solve this problem, we can use the formula for the sum of an arithmetic progression (AP), which is given by:
Sum = (n/2)(first term + last term),
where n is the number of terms.
In this case, the sum of the terms is given as 34, the first term is 3, and the last term is 48. We can substitute these values into the formula to find the number of terms (n):
34 = (n/2)(3 + 48).
Now, let's solve this equation step by step:
1. Simplify the equation:
34 = (n/2)(51).
2. Multiply both sides of the equation by 2 to eliminate the fraction:
34 * 2 = n * 51.
3. Simplify further:
68 = n * 51.
4. Divide both sides of the equation by 51 to isolate n:
68/51 = n.
5. Calculate the value of n:
n ≈ 1.333.
Since the number of terms must be a whole number, we can conclude that the given AP does not have a finite number of terms that can yield a sum of exactly 34.