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Question
If the sum of first m terms of an AP is ( 2m2 + 3m) then what is its second term?
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Solution
Let Sm denotes the sum of first m terms of the AP.
∴ sm = 2m2 +3m
`⇒ s_(m-1) = 2 (m -1)^2 +3 (m-1) = 2( m^2 - 2m +1) +3 (m-1) = 2m^2 - 3-1`
Now,
`m^(th) "term of A"P, a_m = s_m - s_(m-1)`
∴ `a_3 = ( 2m^2 + 3m ) - (2m^2 - m -1 ) = 4m +1`
Putting m = 2,we get
`a_2 = 4 xx 2 +1 = 9`
Hence, the second term of the AP is 9.
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