Prove that the difference of the sum of the first n terms and the sum of the next n terms of an arithmetic sequence with common difference d is n*nd
Sum of first n terms is a + a+d+....+ a+(n-1)d= number of terms/2(first term + last term)=n/2(a+a+(n-1)d)= n/2(2a+(n-1)d)Next n terms sum is a+nd + a+(n+1)d + a+(n+2)d +.. a+(2n-1)d=number of terms/2(first term + last term)=n/2(a+nd+a+(2n-1)d) = n/2(2a+nd+(2n-1)d) difference between them is n/2(2a+nd+(2n-1)d) - n/2(2a+(n-1)d)=n*n*d
Prove that the difference of the sum of the first n terms and the sum of the next n terms of an arithmetic sequence with common difference d is n*nd
മറുപടിഇല്ലാതാക്കൂSum of first n terms is a + a+d+....+ a+(n-1)d
മറുപടിഇല്ലാതാക്കൂ= number of terms/2(first term + last term)=n/2(a+a+(n-1)d)= n/2(2a+(n-1)d)
Next n terms sum is a+nd + a+(n+1)d + a+(n+2)d +.. a+(2n-1)d
=number of terms/2(first term + last term)=
n/2(a+nd+a+(2n-1)d) = n/2(2a+nd+(2n-1)d)
difference between them is
n/2(2a+nd+(2n-1)d) - n/2(2a+(n-1)d)
=n*n*d