the fourth term if an A.p is 65 and its seventh term is 80 what is the sum of it's first term a and common difference b,?
a+3b=65
a+6b=80
3b=15
b=5
what is a
get the value of a
and then say (a+b)=?
in other words, what's the 2nd term?
three CD's from 65 is 80 ...CD = (80 - 65) / 3
65 is the 4th term ... the 2nd term is two CD's less
Let's denote the first term by 'a' and the common difference by 'b' in the given arithmetic progression (A.P).
Given that the fourth term of the A.P is 65, we can use the formula for the general term of an A.P to find the value of 'a':
a + 3b = 65 ...........(1) [Using the formula for the fourth term]
Similarly, given that the seventh term of the A.P is 80, we can use the same formula to find the value of 'a':
a + 6b = 80 ...........(2) [Using the formula for the seventh term]
To find the values of 'a' and 'b', we can solve these two equations simultaneously.
Subtracting equation (1) from equation (2), we get:
(a + 6b) - (a + 3b) = 80 - 65
3b = 15
b = 5
Substituting the value of 'b' back into equation (1):
a + 3(5) = 65
a + 15 = 65
a = 50
So the first term of the A.P is 50 and the common difference is 5.
To find the sum of the first term ('a') and the common difference ('b'), we simply add them together:
Sum = a + b
Sum = 50 + 5
Sum = 55
Therefore, the sum of the first term ('a') and the common difference ('b') is 55.
To find the sum of the first term (a) and common difference (b) of an Arithmetic Progression (A.P.), we need to use the given information about the terms.
Given:
Fourth term (n=4) of the A.P. = 65
Seventh term (n=7) of the A.P. = 80
The formula to find the nth term (Tn) of an A.P. is:
Tn = a + (n-1)b
Using this formula, we can form two equations to represent the given information:
Equation 1: T4 = 65
65 = a + 3b
Equation 2: T7 = 80
80 = a + 6b
Now, we have a system of equations with two variables. We can solve these equations simultaneously to find the values of a and b.
To solve the system of equations, we can use any method like substitution or elimination. Here, we will use the elimination method to solve this system.
Multiply Equation 1 by 2:
2(65) = 2(a + 3b)
130 = 2a + 6b
Now, subtract Equation 2 from the above equation:
130 - 80 = (2a + 6b) - (a + 6b)
50 = a
Substitute the value of a in Equation 1:
65 = 50 + 3b
15 = 3b
b = 5
Therefore, the sum of the first term (a) and common difference (b) is:
a + b = 50 + 5 = 55