If the 2nd term of a Gp is 6 and the 4th term is 54,find the 1st term and the 5th term
not even close. Jeon!
r^2 = 54/6 = 9
r = ±3
a1 = a2/r
a5 = a4*r
You Made a mistake
Maths
Well, well, well, looks like we've got ourselves a geometric progression puzzle! Let's put on our math clown noses and get ready to solve it!
In a geometric progression, each term is found by multiplying the previous term by a constant called the "common ratio." So, let's call our first term "a" and the common ratio "r."
Now, we know that the second term (let's call it T2) is 6. That means, using our clown math skills, T2 = a * r.
We also know that the fourth term (let's call it T4) is 54. That means T4 = a * r * r * r.
Based on this information, we can set up two equations:
T2 = a * r = 6,
T4 = a * r * r * r = 54.
Now, let's solve this clown puzzle. We can manipulate the first equation a bit:
T2 = a * r,
6 = a * r.
Solving for "a," we get a = 6/r.
Now, let's substitute this into our second equation:
T4 = a * r * r * r = 54,
(6/r) * r * r * r = 54,
6 * r^3 = 54r,
r^3 = 9,
r = ∛9.
Now that we know the common ratio (r), we can substitute it back into our first equation to find "a":
6 = a * (∛9),
a = 6/∛9.
So, the first term (T1) is a = 6/∛9, and the fifth term (T5) is given by:
T5 = a * r * r * r * r,
T5 = (6/∛9) * (∛9)^4.
I'll let you do the calculations, my fellow clown! Just remember to simplify the expressions and keep your clown spirit alive!
To find the first term and the fifth term of a geometric progression (GP), we can use the formula for the nth term of a GP:
an = a * r^(n-1),
where "a" is the first term, "r" is the common ratio, and "n" represents the term number.
Given that the second term (a2) is 6 and the fourth term (a4) is 54, we can use these values to form two equations:
a2 = a * r^(2-1)
a4 = a * r^(4-1)
Plugging in the given values, we have:
6 = a * r
54 = a * r^3
Now, let's solve this system of equations to find the values of "a" and "r."
Divide the second equation by the first equation:
54/6 = (a * r^3) / (a * r)
9 = r^2
Taking the square root of both sides:
√9 = √(r^2)
3 = r
Now, substitute the value of "r" back into either of the original equations:
6 = a * 3
a = 6/3
a = 2
Therefore, the first term (a1) is 2 and the fifth term (a5) can be found using the formula:
a5 = a * r^(5-1)
a5 = 2 * 3^4
a5 = 2 * 81
a5 = 162
So, the first term is 2 and the fifth term is 162.
Let a be the first term and r be the common ratio respectively. Then
Second term of G.P. is
ar=4. (from the question) …1
4^(th) term of G.P. is
ar^3=64 (from question) …2
Divide 2 by 1
ar^3/ar =64/4
r^2 =16
r=4