The arithmetic progression has first term 4 and last term 34. If the sum of its terms is 247, find the number of terms and their common difference.
n/2 (4+34) = 247
n=13
I expect you can now find the difference, eh?
To solve this problem, we need to find the number of terms in the arithmetic progression and the common difference.
Let's start by finding the number of terms:
The formula for the sum of an arithmetic progression is given by:
Sum = (number of terms / 2) * (first term + last term)
We are given that the sum of the terms is 247, and the first term is 4, and the last term is 34. Let's plug in these values into the formula and solve for the number of terms:
247 = (number of terms / 2) * (4 + 34)
Simplifying the equation:
247 = (number of terms / 2) * 38
Now, we can solve for the number of terms by isolating it:
(number of terms / 2) * 38 = 247
Multiplying both sides by 2:
number of terms * 38 = 494
Dividing both sides by 38:
number of terms = 494 / 38
Calculating:
number of terms ≈ 13
So, we have found that there are approximately 13 terms in the arithmetic progression.
Now let's find the common difference:
The common difference (d) is the difference between any two consecutive terms in an arithmetic progression.
We are given that the first term is 4 and the last term is 34. The difference between these two terms is 34 - 4 = 30.
So, the common difference is 30.
To summarize:
- The number of terms in the arithmetic progression is approximately 13.
- The common difference in the arithmetic progression is 30.