in an ap the 10thterm is 68 while it 4th term is 26 find the common different and the ist term
How about just using our definitons
"the 10thterm is 68" ----> a + 9d = 68
"the 4th term is 26 " ----> a + 3d = 26
subtract them:
6d = 42
d = 7
back in a + 3d = 26
a + 21 = 26
a = 5
btw, Its called common difference, not different.
six differences between 4th and 10th ... d = (68 - 26) / (10 - 4)
1st = 4th - 3 d
To find the common difference and the first term in an arithmetic progression (AP), we need to use the given information about the 4th term and the 10th term.
Let's denote the common difference as 'd' and the first term as 'a'.
Given:
The 4th term (a + 3d) = 26
The 10th term (a + 9d) = 68
Now, we can solve these two equations to find the values of 'd' and 'a'.
Equation 1: (a + 3d) = 26
Equation 2: (a + 9d) = 68
We can start by subtracting Equation 1 from Equation 2 to eliminate 'a':
(a + 9d) - (a + 3d) = 68 - 26
6d = 42
Dividing both sides by 6, we get:
d = 42 / 6
d = 7
So, the common difference 'd' is 7.
Now, substitute the value of 'd' back into one of the original equations to find 'a'.
Using Equation 1: (a + 3d) = 26
(a + 3*7) = 26
(a + 21) = 26
Subtracting 21 from both sides, we have:
a = 26 - 21
a = 5
Hence, the first term 'a' is 5.
To summarize:
- The common difference (d) in the arithmetic progression is 7.
- The first term (a) in the arithmetic progression is 5.