Question

deduce s base n=n/2[a+a base n] from the formula s base n=n/2[2a+(n-1)d]

Answer 1

we know
$a |n| = a + (n - 1)d .....(1)$
Now sum is given by
$s |n| = \frac{n}{2} (2a + (n - 1)d) \\ s |n| = \frac{n}{2} (a + a + (n - 1)d) \\ from \: eqn \: (1) \\ s |n| = \frac{n}{2} (a + a |n| )$
hence proved
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