The ratio of the sums of first m and first n of an AP is m²:n². Show that the ratio of its mth and nth terms is (2m-1):(2n-1)
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The ratio of the sums of first m and first n of an AP is m²:n². Show that the ratio of its mth and nth terms is (2m-1):(2n-1)
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Step-by-step explanation:
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Step-by-step explanation:
Let Sm and Sn be the sum of the first m and first n terms of the AP respectively. Let, a be the first term and d be a common difference.
m/2[2a+(m-1)d]. m
___________. =. n
n/2 [2a+(n-1)d].
2a + (m-1) d. m
__________ = n
2a + (n-1) d