The 3rd and 9th term of a G.p are 54 and 39366 respectively.find the (a 6th term (b)sum of the 4th and 7th term (c)product of 2nd and 5th term
geez -- once is enough already.
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To find the missing terms in a geometric progression (G.P.), we can use the formula:
𝑎𝑛 = 𝑎₁ * 𝑟^(𝑛−1)
Where 𝑎𝑛 represents the 𝑛-th term of the G.P., 𝑎₁ is the first term of the G.P., 𝑟 is the common ratio, and 𝑛 is the position of the term.
We have the 3rd and 9th terms, so we can set up two equations using this formula:
𝑎₃ = 𝑎₁ * 𝑟^(3−1) ----(1)
𝑎₉ = 𝑎₁ * 𝑟^(9−1) ----(2)
Given 𝑎₃ = 54 and 𝑎₉ = 39366, we can substitute these values into the equations above:
54 = 𝑎₁ * 𝑟^(2)
39366 = 𝑎₁ * 𝑟^(8)
Now we can solve these two equations simultaneously to find the values of 𝑎₁ and 𝑟.
To find the 6th term (𝑎₆), we substitute 𝑛 = 6 into our formula:
𝑎₆ = 𝑎₁ * 𝑟^(6−1) ----(3)
To find the sum of the 4th and 7th terms, we substitute 𝑛 = 4 and 𝑛 = 7 into our formula:
𝑎₄ + 𝑎₇ = 𝑎₁ * 𝑟^(4−1) + 𝑎₁ * 𝑟^(7−1) ----(4)
To find the product of the 2nd and 5th terms, we substitute 𝑛 = 2 and 𝑛 = 5 into our formula:
𝑎₂ * 𝑎₅ = 𝑎₁ * 𝑟^(2−1) * 𝑎₁ * 𝑟^(5−1) ----(5)
By solving equations (1) and (2) to find 𝑎₁ and 𝑟, we can then substitute these values into equations (3), (4), and (5) to calculate the missing values.