Question

Find the sum of odd numbers between 0 to 50 in AP
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Answer 1

Answer:

625

Step-by-step explanation:

sum = 1 + 3 + 5 + 7 + ......+49.

this is an A.P, whose first term(a) = 1 and last term(Tn) = 49.

common difference(d) = 3-1 = 2

Total no. of odd number lie b/w 0 and 50 = n

but,

Tn = a + (n-1)d

or, 49 = 1 + (n-1)2

or, n-1 = 48/2 =24

n = 25

hence

sum = n/2(a + Tn)

sum = 25(1 + 49)/2

sum = 25×50/2 = 25×25

sum = 625

Answer 2

Answer:

a + ( n - 1) d = an

=> 1 + ( n - 1) 2 = 49

=> ( n - 1) 2 = 48

=> ( n - 1) = 24

=> n = 25.

So,

Sn = n/2 × ( a +l)

= 25 /2× ( 1 +49)

= 25 /2 × 50

= 25 ×25

= 62