If the ratio of the sum of first [tex]n[/tex] terms of two A.P's is
[tex](7n+1)\colon(4n+26)[/tex], find the ratio of their [tex]{m}^{th}[/tex] terms.
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If the ratio of the sum of first [tex]n[/tex] terms of two A.P's is
[tex](7n+1)\colon(4n+26)[/tex], find the ratio of their [tex]{m}^{th}[/tex] terms.
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Answer:
(14m - 6) : (8m +22)
Step-by-step explanation:
Let a₁,a₂ be the first terms and d₁,d₂ be the common differences of the two given AP's. The sum of n terms is given by:
Given that Sum of first n terms is (7n + 1):(4n + 26).
To find the ratio of the mth terms of the two given AP's, we replace n by (2m - 1), we get
∴ Therefore, ratio of the mth terms of the two Ap's is (14m - 6) : (8m + 22).
Hope it helps!