The different between the 11th term of an AP is 49 and if the 11th term is 74/25 times the 4th term determine ,the common difference ,the first term of the sequence and the 6th term of the sequence
How did u gett 222d
T11-T4=49
a+10d-(a+3d)=49
a+10d-a-3d=49
10d-3d=49
7d=49
d=7
T11=74/25×T4
a+10d = 74/25×a+3d
a+10d=74a+222d
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25
25(a+10d)=74a+222d
25a+250d=74a+222d
25a-74a=222d-250d
-49a=-196
a=4
Where a is first num
d is common difference
6th term = a + 5d
Then substitute
The difference between the 11th term and 4th of an A.P is 49 and if the 11th term is 74 times the fourth term determine A the common difference B first term
74 times 3
Favour
To find the common difference, first, we need to determine the value of the 11th term and the 4th term.
Let's assume that the first term of the sequence is 'a' and the common difference is 'd'.
We are given two pieces of information:
1. The difference between the 11th term and the 4th term is 49:
The difference between any two terms in an arithmetic progression (AP) is constant and equal to the common difference. So, we can write:
11th term - 4th term = 49
Using the formula for the nth term of an AP:
(4-1)d = 49
3d = 49
d = 49/3
2. The 11th term is 74/25 times the 4th term:
We can use this information to form another equation:
11th term = 4th term + (74/25) * 4th term
= 4th term * (1 + 74/25)
= (99/25) * 4th term
Since we now have two equations, we can solve them simultaneously to find the value of the 4th term. Let's proceed with solving the equations:
Equation 1: 3d = 49
Substitute the value of d we obtained earlier:
3 * (49/3) = 49
49 = 49 (this equation is true)
Therefore, the common difference (d) is 49/3.
Equation 2: 11th term = (99/25) * 4th term
Substitute the value of d:
11th term = (99/25) * (4th term)
11th term = (99/25) * (1d) (since d = 4th term)
11th term = (99/25) * (49/3) (substituting the value of d)
To find the value of the 11th term, we simplify the expression:
11th term = (99 * 49) / (25 * 3)
11th term = 4851/25
Now that we know the common difference and the 11th term, we can find the first term and the 6th term.
To find the first term (a), we use the formula for the nth term:
11th term = a + (n - 1)d
Substituting the values:
4851/25 = a + (11 - 1) * (49/3)
4851/25 = a + 10 * (49/3)
4851/25 = a + 490/3
Simplifying further:
4851/25 - 490/3 = a
(3 * 4851 - 25 * 490) / (3 * 25) = a
16353/75 = a
Therefore, the first term (a) is 16353/75.
To find the 6th term, we use the formula for the nth term:
6th term = a + (n - 1)d
Substituting the values:
6th term = (16353/75) + (6 - 1) * (49/3)
6th term = (16353/75) + 5 * (49/3)
Simplifying further:
6th term = (16353/75) + (245/3)
6th term = (16353 + 245 * 25) / (75 * 3)
Calculating:
6th term = 18428/75
Therefore, the 6th term is 18428/75.
"The difference between the 11th term of an AP is 49"
makes no sense.
difference between T11 and what?
but the second criterion is
a+10d = 74/25 (a+3d)