The third and sixth term of a G.P are 48&14 2/9.find the fifth term.write down the first four term of the G.P
To find the common ratio (r) in a geometric progression (G.P), we can use the formula:
r = (6th term) / (3rd term)
In this case, the 6th term is 14 2/9 and the 3rd term is 48.
r = (14 2/9) / (48)
Step 1: Convert the mixed fraction (14 2/9) to an improper fraction.
14 2/9 = (9 * 14) + 2 / 9 = 126/9 + 2/9 = 128/9
Now we can plug in the values to find r:
r = (128/9) / (48)
Step 2: Simplify the expression by dividing the numerator by the denominator.
r = (128/9) * (1/48)
r = 128 / (9 * 48)
r = 4/27
Now that we have the common ratio (r = 4/27), we can find the fifth term of the G.P.
The formula to find the nth term of a G.P is:
nth term = a * (r ^ n-1)
In this case, n = 5, and we need to find the 5th term.
If the 3rd term is 48, we can write the equation as:
48 * (4/27)^(5-1)
48 * (4/27)^4
48 * (256/729)
To multiply fractions, multiply the numerators and multiply the denominators:
48 * 256 / 27^4 * 729
The first four terms of the G.P will be:
1st term: 48
2nd term: 48 * (4/27)^1
3rd term: 48 * (4/27)^2
4th term: 48 * (4/27)^3
Simplifying the expression in the fifth term, we get:
48 * 256 / (27 * 27 * 27 * 27) = 12288 / 531441
Therefore, the fifth term of the G.P is 12288/531441.