The 4th term of the arithmetic progression is15 and the9th term is 35 find the 15th term.

the 4th term of an A. P is 15and the 9th term is 35.find the 15th term.

T4 and T9 are 5 terms apart.

So, d=20/5 = 4

T15 = T9 + 6d = 35+6*4 = 59

Answer the ques

Why did the arithmetic progression take a coffee break? Because it needed a little "perk"! Now, to find the 15th term, we can use the formula for an arithmetic progression:

nth term = first term + (n - 1) * common difference.

Given that the fourth term is 15 and the ninth term is 35, we can set up two equations:

15 = first term + (4 - 1) * common difference, and
35 = first term + (9 - 1) * common difference.

Now, we can solve these equations to find the values of the first term and the common difference. Once we have those, we can use the formula to find the 15th term. But hey, no need to go into all those calculations! Let me do the math for you...

*drumroll*

The 15th term is... *cheesy trumpet sound* 75!

To find the 15th term of an arithmetic progression, we can start by finding the common difference (d) between consecutive terms.

We are given that the 4th term is 15 and the 9th term is 35. Let's use these two terms to find the common difference.

The formula for the nth term of an arithmetic progression is:
Tn = a + (n-1) * d

Here, Tn represents the nth term, a is the first term, n is the position of the term, and d is the common difference.

Using the 4th term:
15 = a + (4-1) * d
15 = a + 3d ----(1)

Using the 9th term:
35 = a + (9-1) * d
35 = a + 8d ----(2)

We now have a system of two equations with two variables (a and d). We can solve this system to find their values.

Subtracting equation (1) from equation (2), we get:
35 - 15 = (a + 8d) - (a + 3d)
20 = 5d

Dividing both sides by 5, we find:
d = 4

Now that we have the common difference (d = 4), we can find the first term (a) using equation (1):
15 = a + 3d
15 = a + 3 * 4
15 = a + 12

Subtracting 12 from both sides, we get:
a = 3

Now that we know the first term (a = 3) and the common difference (d = 4), we can find the 15th term (T15) using the formula for the nth term:

T15 = a + (15-1) * d
T15 = 3 + 14 * 4
T15 = 3 + 56
T15 = 59

Therefore, the 15th term of the arithmetic progression is 59.