if the 8th term of an A.P is twice the 5th term, find the 12th term
What subject is "francis"?
the 8th term of an A.P is twice the 5th term
----> a + 7d = 2(a+4d)
a+7d = 2a + 8d
a = -d
12th term = a + 11d
= -d + 11d
= 10d
e.g. let d = 4, then a = -4
term(8) = -4 + 7(4) = 24
term(5) = -4 + 4(4) = 12
so term 8 is twice term 5
term 12 = -4+11(4) = 40 which is 10d or 10(4)
As you can see there is so unique answer to your problem, just let d equal anything you want, as long as "a" is its opposite, it will work
To find the 12th term of an arithmetic progression (A.P) when the 8th term is twice the 5th term, we need to first determine the common difference.
Let's assume that the first term of the A.P is "a" and the common difference is "d".
According to the information given, the 8th term, which is a + 7d, is twice the 5th term, which is a + 4d.
So, we can set up the equation: a + 7d = 2(a + 4d).
Now, let's solve this equation step-by-step to find the values of "a" and "d":
a + 7d = 2a + 8d [Distribute 2 to a and 4d]
7d - 8d = 2a - a [Combine like terms]
-d = a [Simplify further]
Now, substituting the value of "a" in terms of "d" in the equation a + 7d = 2(a + 4d):
-d + 7d = 2(-d + 4d) [Substitute a with -d]
6d = 6d [Simplify]
This equation does not provide any new information. Therefore, the value of "d" can be any real number, which means that the common difference could be any real number.
Now that we have determined that the common difference "d" can be any value, we can find the 12th term.
The formula to find the nth term of an arithmetic progression is: a + (n - 1) * d, where "a" is the first term and "d" is the common difference.
The 12th term can be calculated as follows:
12th term = a + (12 - 1) * d [Substitute n = 12]
Depending on the given value for the first term "a" and the common difference "d", substitute these values into the equation to find the 12th term.
To find the 12th term of an arithmetic progression (A.P.), we first need to determine the common difference (d) between any two consecutive terms. Given that the 8th term is twice the 5th term, we can use this information to find the value of the common difference.
Let's assume that the 5th term of the A.P. is represented by 'a'. Therefore, the 8th term would be '2a' since it is twice the 5th term.
The formula to find the nth term (Tn) of an A.P. is:
Tn = a + (n - 1) * d
For the 5th term, n = 5. Plugging in these values into the formula, we have:
a + (5 - 1) * d = a + 4d
Similarly, for the 8th term, n = 8. Plugging in the values, we have:
2a = a + 7d
Now, we can set up an equation using the information we have:
a + 4d = 2a + 7d
Simplifying the equation, we get:
3d = a
This equation shows us that the value of the common difference (d) is equal to one-third of the 5th term (a).
To find the 12th term, we can substitute the values of 'a' and 'd' into the formula for the nth term:
T12 = a + (12 - 1) * d
T12 = a + 11d
Since we know that 3d = a, we can substitute this into the equation:
T12 = 3d + 11d
T12 = 14d
Therefore, the 12th term of the A.P. is 14 times the common difference.