Question

a natural number which cannot be expressed as a sum of successive odd natural numbers starting with 1 is not a what​

Answer 1

ANSWER

We have

3+5+7+9+..... to n terms =48

We know that

Sn=2n[2a+(n−1)d]

here a=3 , d=2 ,Sn=48

⇒2n[2×3+(n−1)×2]=48 

⇒n(3+n−1)=48⇒n2+2n−48=0⇒n2+8n−6n−48=0

⇒n(n+8)−6(n+8)⇒(n+8)(n−6)=0⇒n=−8orn=6

∵ n can not be a negative here 

∴ n=6

Answer 2

Answer: If a natural number cannot be expressed as a sum of successive odd natural numbers starting with 1, then it is not a perfect square..