Find the maximum sum of the A.P. $40 + 38 + 36 + 34 + 32 +$ ________.

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Solution

$F o r max i m u m s u m o f A . P . u p t o 0 A . P 40 + 38 + 36 + 34 + . . . . . . . . . . + 0 F i r s t t e r m = 40 c o m m o n d i f f e r e n c e = 38 - 40 = - 2 \Rightarrow a_{n} = 0 \Rightarrow a_{n} = a + (n - 1) d \Rightarrow 0 = 40 + (n - 1) \times - 2 \Rightarrow - 40 = - (n - 1) \times 2 \Rightarrow 20 = n - 1 n = 21 ∴ m a x i m u m s u m i s S_{21} = \frac{21}{2} [2 \times 40 + (21 - 1) \times - 2] \Rightarrow \frac{21}{2} [80 - 40] \Rightarrow 21 \times 20 = 420$

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Find the maximum sum of the A.P. 40+38+36+34+32+________.

FormaximumsumofA.P.upto0A.P40+38+36+34+..........+0Firstterm=40commondifference=38−40=−2⇒an=0⇒an=a+(n−1)d⇒0=40+(n−1)×−2⇒−40=−(n−1)×2⇒20=n−1n=21∴maximumsumisS21=212[2×40+(21−1)×−2]⇒212[80−40]⇒21×20=420

Find the maximum sum of the A.P. $40 + 38 + 36 + 34 + 32 +$ ________.