Question

find the sum of all odd positive integers less than 450​

Answer 1

AP:1,3,5,....,449.

Here, a= 1,d=2

an=449

a+(n-1)d=449

1+(n-1)2=449

n-1=448/2

n-1=221

n=222

S222=222/2(2×1+221×2)

=111(443)

=49173

Therefore,sum of all odd positive number less the 450 =49173

Answer 2

Answer:

Odd positive integers less that 450 are

1,3,5,7,9,11,......449

S = 1 + 3 + 5 + 7 + .......... + 449

This is an Arithmetic series with first term a = 1,

Common Difference does = 2, last term l = 449

Number of terms n = l - a/d + 1

n = 449 - 1/2 + 1

n = 448/2 + 1

= 224 + 1 = 225

Sn = n/2 (a + l)

Sn = 225/2 (1 + 449)

S = 225/2 (1 + 449)

= 225/2 × 450 = 225 × 225

S = 50,625

∴ Sum of positive integers less than 450 is 50,625.

Step-by-step explanation:

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