The 3rd term and 9th term of a G.P are 54 and 39,366 respectively.Find the:6th term,sum of the 4th and 7th term and product of 2nd and 5th term?
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To find the common ratio (r) of the geometric progression (G.P.), we can use the formula:
r = (9th term) / (3rd term)
In this case, the 9th term is 39,366 and the 3rd term is 54, so:
r = 39,366 / 54
Next, let's calculate the common ratio (r):
r = 729
Now that we have the common ratio, we can find the other terms.
To find the 6th term, we can use the formula:
6th term = (3rd term) * (r^(6-3))
Plug in the values:
6th term = 54 * (729^(6-3))
Simplifying:
6th term = 54 * 729^3
To find the sum of the 4th and 7th term, we can use the formula:
Sum of n terms (Sn) = (first term) * ((r^n - 1) / (r - 1))
Let's calculate the sum of the 4th term:
4th term = (first term) * (r^3)
Sum of the 4th term = (first term) * ((r^4 - 1) / (r - 1))
Now, let's calculate the sum of the 7th term using the same formula:
7th term = (first term) * (r^6)
Sum of the 7th term = (first term) * ((r^7 - 1) / (r - 1))
To find the product of the 2nd and 5th term, we simply multiply them together:
Product of 2nd and 5th term = (2nd term) * (5th term)
Multiply the resulting values from each calculation to get the answers to your question.
54 r^6 = 39366 ... r^6 = 729 ... looks like the ratio (r) is 3
start with the 3rd term , and keep multiplying by 3
you'll have to divide by 3 to find the 2nd term
the two terms are 6 apart, so
r^6 = 39366/54 = 729
r = ±3
So now you want to find a, and then
a_6 = ar^5
a_4 + a_7 = ar^3(1+r^3)
a_2 * a_5 = a^2 r^5