the 6th term of an AP is 15 and the 8th term is 27 find the 5th term
These are routine questions, you jus HAVE TO know how to do these.
term6 = a + 5d = 15, just using the definitions
term8 = a + 7d = 27
subtract them:
2d =12
d = 6
sub back: a + 5d = 15
a + 30 = 15
a = -15
term5 = a + 4d = .....
To find the 5th term of the given arithmetic progression (AP), we need to determine the common difference (d) first.
We are given that the 6th term is 15 and the 8th term is 27. From this information, we can deduce the following:
The 6th term (a₆) = a + 5d = 15
The 8th term (a₈) = a + 7d = 27
Now, we can solve these two equations simultaneously to find the common difference (d):
a + 5d = 15 (equation 1)
a + 7d = 27 (equation 2)
Subtracting equation 1 from equation 2, we get:
(a + 7d) - (a + 5d) = 27 - 15
2d = 12
d = 6
Now that we have found the common difference (d = 6), we can substitute this into either equation 1 or equation 2 to find the value of 'a' (the first term).
Let's substitute 'd' into equation 1:
a + 5d = 15
a + 5(6) = 15
a + 30 = 15
a = 15 - 30
a = -15
Therefore, the first term (a) is -15 and the common difference (d) is 6.
Now we can calculate the 5th term (a₅) of the AP using the formula:
aₙ = a + (n - 1)d
Substituting the values we found:
a₅ = -15 + (5 - 1)6
a₅ = -15 + 4(6)
a₅ = -15 + 24
a₅ = 9
Hence, the 5th term of the arithmetic progression (AP) is 9.
To find the 5th term of an arithmetic progression (AP), we can use the given information about the 6th and 8th terms.
Let's denote the first term of the AP as "a" and the common difference between the terms as "d".
Given:
The 6th term is 15:
a + 5d = 15 ----(Equation 1)
The 8th term is 27:
a + 7d = 27 ----(Equation 2)
We have two equations with two variables (a and d). Let's solve this system of equations simultaneously.
Subtracting Equation 1 from Equation 2, we get:
(a + 7d) - (a + 5d) = 27 - 15
2d = 12
d = 12/2
d = 6
Substituting the value of d into Equation 1, we have:
a + 5(6) = 15
a + 30 = 15
a = 15 - 30
a = -15
Now we have the values of the first term (a = -15) and the common difference (d = 6).
To find the 5th term of the AP, we can use the formula:
nth term = a + (n - 1)d, where n represents the position of the term.
Therefore, the 5th term (n = 5) will be:
5th term = -15 + (5 - 1)6
5th term = -15 + 4*6
5th term = -15 + 24
5th term = 9.
So, the 5th term of the given AP is 9.