Question

find the sum of odd no.s between 0 and 50​

Answer 1

First odd number,a = 1

Difference between each odd number,d = 2

Last odd integer less than 50, l = 49

Now,

a + (n-1)d = 49

1 + 2n - 2 = 49

2n = 50

n = 25 ( There are 25 odd numbers b/w 0 and 50 )

Now,

Sum of these numbers = n/2 { a + l }

=> 25/2 × { 1 + 49 }

=> 25/2 × 50

=> 25 × 25

=> 625

Hence, Sum is 625

Answer 2

Answer:

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Step-by-step explanation:

$first \: odd \: no. = 1(a) \\ last \: odd \: no. = 49(l)$

$by \: ap \: \: l = a + (n - 1)d \\ commom \: difference = d = 2 \\ 49 = 1 + (n - 1)2 \\ 48 = (n - 1)2 \\ n - 1 = 24 \\ n = 25terms$

$sum \: of \: ap = \\ sn \: = \frac{n}{2}(2a + (n - 1)d) \\ sn = \frac{25}{2}(2 \times 1 + 24 \times 2) \\ = \frac{25}{2} (2 + 48) \\ = \frac{25}{2} \times 50 \\ = 25 \times 25 = 625(ans)$

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