on @ Gp.the 4th term exceed 3rd term by 72 nd 3rd term exceeds 2nd term by 24.fnd the frst four term of the progressn.
just use what you know about GPs:
ar^3 = ar^2+72
ar^2 = ar+24
So,
ar^2(r-1) = 72
ar(r-1) = 24
Now divide and you have r=3
So, a=4
and the GP is 4,12,36,108
To find the first four terms of the progression, let's call the first term "a" and the common difference "d".
According to the given information:
The 4th term exceeds the 3rd term by 72:
a + 3d = a + 4d - 72
d = 72
The 3rd term exceeds the 2nd term by 24:
a + 2d = a + 3d - 24
d = 24
From the two equations, we have found two different values for "d" (72 and 24). This means there may have been a mistake in the question.
Please double-check the given information and provide the correct values so that I can help you find the first four terms of the progression.
To find the first four terms of the progression, we need to determine the common difference and the first term.
Let's start by denoting the first term as "a" and the common difference as "d".
We are given that the fourth term exceeds the third term by 72. Therefore, we can write the equation:
a + 3d = a + 72
We are also given that the third term exceeds the second term by 24. Therefore, we can write the equation:
a + 2d = a + 24
Now we have a system of two equations with two unknowns:
a + 3d = a + 72
a + 2d = a + 24
Simplifying these equations further:
3d = 72
2d = 24
Dividing both sides of the first equation by 3, we find:
d = 24
Now substitute the value of "d" into the second equation:
2(24) = a + 24
48 = a + 24
Subtracting 24 from both sides of the equation, we find:
a = 24
Therefore, the common difference (d) is 24, and the first term (a) is also 24.
Now we can find the first four terms of the progression:
First term: a = 24
Second term: a + d = 24 + 24 = 48
Third term: a + 2d = 24 + 2(24) = 72
Fourth term: a + 3d = 24 + 3(24) = 120
So, the first four terms of the progression are 24, 48, 72, and 120.