4th and 7 terms of a G.P. are 1/18 and -1/ 486 respectively. Find the G.P.
My solution:
ar^3=1/18.... eq no1
ar^6=-1/486...eq no2
ar^6/ar^3 = -1/486÷1/18
r^3=-1/27
r=-1/3
Place this value in equation 1
ar^3=1/18
a*-1/3^3=1/18
a*-1/27=1/18
a=-7/6
Required GP:
a=-7/6
ar=-7/6*1/3=-7/18
-7/6,-7/18.......n =ans
My answer is not correct please tell me the correct answer
a*-1/27=1/18
a=-7/6
Bzzzt.
a = -3/2
To find the correct answer, let's go through the steps again:
Given that the 4th term of the geometric progression (GP) is 1/18, we can write the equation as:
a * r^3 = 1/18 .............(1)
And given that the 7th term of the GP is -1/486, we can write the equation as:
a * r^6 = -1/486 .............(2)
To eliminate 'a' from the equations, let's divide equation (2) by equation (1):
(r^6) / (r^3) = (-1/486) / (1/18)
r^3 = -1/27
Take the cube root of both sides to find the value of 'r':
r = -1/3
Now, substitute the value of 'r' in equation (1) to find the value of 'a':
a * (-1/3)^3 = 1/18
a * (-1/27) = 1/18
Multiply both sides by 27 to solve for 'a':
a * -1 = 27/18
a = -27/18
Simplify 'a':
a = -3/2
Now, we have the first term 'a' as -3/2 and the common ratio 'r' as -1/3. Therefore, the geometric progression is:
-3/2, -1/2, 1/6, 1/18, ...