Question

Find the sum of 54+52+50+....+10​

Answer 1

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• Since this is a decreasing A.P. with first term positive, the maximum sum will occur upto the point where the progression remains non-negative. 54, 52, 50, ….. 0 Hence, 28 terms × 27 = 756.

Answer 2

Step-by-step explanation:

it is an ap,where,

$a = 54$

$d = - 2$

$last \: term \: {l} = 10$

using formula

$l = a + (n - 1)d$

$10 = 54 + (n - 1) \times - 2$

$- 44 = (n - 1) \times - 2$

$n = 23$

now,using formula for sum

$sn = \frac{n}{2} \times (a + l)$

$sn = \frac{23}{2} (54 + 10)$

$sn = \frac{23}{2} \times 64$

$sn = 23 \times 32$

$sn = 736$

hope it helps