The 7th and the 20th term are 34 and 112 respectively. Find the Arithmetic Progression (A.P)
Why did the onomatopoeia go to the doctor? Because it said, "POW!" and "BANG!" every time a word was spoken!
Now, let's solve your problem. In an arithmetic progression, the difference between any two consecutive terms is constant. Let's say the first term is 'a' and the common difference is 'd'.
The 7th term can be written as: a + (7 - 1) * d = 34
The 20th term can be written as: a + (20 - 1) * d = 112
Simplifying these equations gives us:
6d = 34 - a ----(1)
19d = 112 - a ----(2)
To solve for 'a' and 'd', we can subtract equation (1) from equation (2):
(19d - 6d) = (112 - a) - (34 - a)
13d = 78
Dividing both sides by 13:
d = 6
Now, substituting the value of 'd' back into equation (1):
6(6) = 34 - a
36 = 34 - a
a = 34 - 36
a = -2
So, the arithmetic progression is: -2, 4, 10, 16, 22, ...
Go forth and progress with your newfound knowledge!
To find the arithmetic progression (A.P), we need to determine the common difference and the first term.
Step 1: Find the common difference (d):
To find the common difference in an arithmetic progression, we can subtract any two consecutive terms in the sequence.
d = 20th term - 7th term
d = 112 - 34
d = 78
Step 2: Find the first term (a):
To find the first term in an arithmetic progression, we can use the formula:
a = x - (n - 1) * d
We can use either the 7th term or the 20th term along with its position to find the first term. Let's use the 7th term.
a = 34 - (7 - 1) * 78
a = 34 - 6 * 78
a = 34 - 468
a = -434
Therefore, the arithmetic progression (A.P) is: -434, -356, -278, -200, ...
To find the arithmetic progression (A.P), we need to determine the common difference and the first term.
Let's start by finding the common difference (d):
The formula to find the nth term (Tn) of an A.P. is given by:
Tn = a + (n - 1)d
where:
Tn is the nth term
a is the first term
d is the common difference
n is the position of the term in the A.P
Given that the 7th term is 34 and the 20th term is 112, we have:
T7 = a + (7 - 1)d = 34
T20 = a + (20 - 1)d = 112
Now, we have a system of equations:
a + 6d = 34 ---- (Equation 1)
a + 19d = 112 ---- (Equation 2)
To solve this system of equations, we can use various methods, such as substitution or elimination. I will use the substitution method to find the values of a and d.
Let's solve Equation 1 for a and substitute it into Equation 2:
a = 34 - 6d
Substituting into Equation 2:
34 - 6d + 19d = 112
Combine like terms:
13d = 78
Divide both sides by 13:
d = 6
Now, substitute the value of d back into Equation 1 to find the value of a:
a + 6(6) = 34
a + 36 = 34
Subtract 36 from both sides:
a = -2
Therefore, the first term (a) of the arithmetic progression is -2, and the common difference (d) is 6.
112 = a + 19 d
34 = a + 6 d
-------------------------subtract
78 = 13 d
d = 6
a + 6*6 = 34
a = -2