A G.PIS SUCH THAT THE 3RD TERM IS 9TIMES THE FIRST TERM,WHILE THE 2ND TERM IS ONE TWENTY FOURTH OF THE 5TH TERM.FIND ITS 4TH TERM
"HE 3RD TERM IS 9TIMES THE FIRST TERM"
---> ar^2 = 9a
r^2 = 9
r = ± 3
"WHILE THE 2ND TERM IS ONE TWENTY FOURTH OF THE 5TH TERM"
ar = (1/24)ar^4
24ar = a r^4
24 = r^3
which contradicts the other value of r
bogus question, check your typing (and your caps lock appears to be stuck)
Impossible.
If a3 > a1 then you cannot have a2 < a5
You did not complete your questions
They said that find its 4th term
To find the fourth term of the geometric progression (G.P.), we need to determine the common ratio (r) first. We can use the given information to find it.
Let's assign the first term as "a" and the common ratio as "r."
Given:
- The third term is 9 times the first term: a * r^2 = 9a (Equation 1)
- The second term is one twenty-fourth of the fifth term: a * r = (1/24) * (a * r^4) (Equation 2)
Now, we can solve these two equations simultaneously to find the values of "a" and "r."
First, let's simplify Equation 2 by canceling out "a":
r = (1/24) * r^4
Next, divide both sides of the equation by r:
1 = (1/24) * r^3
Multiply both sides by 24:
24 = r^3
Now, take the cube root of both sides:
r = ∛24
Hence, the common ratio (r) is the cube root of 24.
Now, to find the fourth term, we can substitute the values of the first term (a) and common ratio (r) into the formula:
Fourth term (a4) = a * r^3
Substituting r = ∛24:
a4 = a * (∛24)^3
Finally, we can simplify:
a4 = a * 24∛2
The value of the fourth term (a4) will depend on the value of the first term (a).