In an A.p , the 1oth term is 68 and the 4th term is 26 .find common different
To find the common difference of an arithmetic progression (A.P.), we need to use the formula for the nth term of an A.P., which is given by:
an = a + (n - 1)d
Where:
an = nth term
a = first term
n = number of terms
d = common difference
We are given that the 10th term (a10) is 68, so we can plug this into the formula:
68 = a + (10 - 1)d
We are also given that the 4th term (a4) is 26, so we can plug this into the formula:
26 = a + (4 - 1)d
Now, we have a system of equations with two unknowns (a and d). We can solve the system to find the values of a and d.
From the equations above, we have:
68 = a + 9d ...(1)
26 = a + 3d ...(2)
To solve this system, we can subtract equation (2) from equation (1):
68 - 26 = (a + 9d) - (a + 3d)
42 = 6d
d = 42/6
d = 7
So, the common difference (d) of the arithmetic progression is 7.
To find the common difference in an arithmetic progression (AP), we can use the formula:
nth term = a + (n - 1)d
Where:
nth term represents any term in the AP,
a represents the first term,
n represents the position of the term,
d represents the common difference.
In this case, we are given the 10th term as 68 and the 4th term as 26. Using the formula, we can set up two equations:
Equation 1: 10th term = a + (10 - 1)d = 68
Equation 2: 4th term = a + (4 - 1)d = 26
Simplifying these equations, we get:
Equation 1: a + 9d = 68
Equation 2: a + 3d = 26
To eliminate 'a' from the equations, we can subtract Equation 2 from Equation 1:
(a + 9d) - (a + 3d) = (68 - 26)
6d = 42
Simplifying further, we divide both sides by 6:
d = 42 / 6
d = 7
Therefore, the common difference in this arithmetic progression is 7.
To find the common difference (d) in an arithmetic progression (AP), we can use the formula:
๐แตสฐ term = ๐ + (๐ โ 1)๐
Where:
๐แตสฐ term is the term number you are looking for in the progression
๐ is the first term of the progression
๐ is the common difference between the terms
We are given:
10th term = 68
4th term = 26
Using the formula for the 10th term:
68 = ๐ + (10 โ 1)๐
68 = ๐ + 9๐ ...(1)
And using the formula for the 4th term:
26 = ๐ + (4 โ 1)๐
26 = ๐ + 3๐ ...(2)
We have two equations with two variables (๐ and ๐). Now, we can solve these equations simultaneously to find the values of ๐ and ๐.
Subtracting equation (2) from equation (1), we get:
68 - 26 = (๐ + 9๐) - (๐ + 3๐)
42 = 6๐
Dividing both sides of the equation by 6, we find:
๐ = 7
Therefore, the common difference (d) in the arithmetic progression is 7.