Find the sum of an A.P of seventeen terms whose middle term is five .

of 17 terms, the middle term is term 9

so
a + 8d = 5 -----> a = 5-8d

sum(17) = (17/2)(2a + 16d)
= (17/2)(10-16d + 16d)
= (17/2)(10)
= 85

Find the sum of 17 term of AP whose middle term is 40

An A.P contains 25 terms.Of the first term is 15 and the least term is 111,find the middle term

Well, if the middle term of the arithmetic progression is five, then I can confidently say that this is one organized bunch of numbers. They're all lined up in a straight line, behaving themselves.

Anyway, since you want to find the sum of the 17 terms, let's call the first term "a" and the common difference "d". Since the middle term is five, that means the 9th term (which is the average of the 8th and 10th term) must also be five. Are you still with me? Great!

So, we can write out the 17-term sequence like this:

a, a + d, a + 2d, a + 3d, ..., a + 8d, 5, a + 10d, ..., a + 15d

Now, since the 9th term is also five, we can say:

a + 8d = 5

But we also have another equation, because we need to find "a". Since the 17th term is the reverse of the first term, we have:

a + 16d = a

Doing some magical math, we can solve these equations and find the values of "a" and "d".

Now that we have both "a" and "d", we can find the sum of the 17 terms using the formula:

Sum = (n/2)(2a + (n-1)d)

Plugging in the values, we get:

Sum = (17/2)(2a + 16d)

And there you have it! The sum of the arithmetic progression with 17 terms whose middle term is five. I hope that puts a smile on your face!

To find the sum of an arithmetic progression (A.P), we need to know the first term, the last term, and the common difference.

In this case, we know that the middle term is 5. Without any further information, we can't determine the exact A.P, as there could be multiple possibilities. However, I can show you how to approach solving this problem once you have those values.

Step 1: Determine the number of terms (n)
Since the A.P has 17 terms, we know that n = 17.

Step 2: Find the common difference (d)
The common difference (d) can be calculated using the middle term, which is 5. As the middle term is the average of the first and last terms, the common difference can be found using the formula:
d = (last term - first term) / (n - 1)
In this case, since we don't know the first and last terms, we can't find the common difference.

Step 3: Find the first term (a) and the last term (l)
Without knowing the common difference, we cannot determine the first and last terms.

Once you have the first term, last term, and common difference, you can use the formula to find the sum of an A.P:

Sum (S) = (number of terms / 2) * (first term + last term)

Find the sum of an a.p of seventeen terms whose middle terms is 5