Magical Mathematics[Interesting Approach]> If the sum of n terms of the AP are n²+n....

If the sum of n terms of the AP are n²+n.show that it is an AP

idrees Ahmad rather , 7 Years ago

Grade 12th pass

3 Answers

Arun

Last Activity: 7 Years ago

If we put n= 1, then we get a₁

Hence a₁ = 1+ 1 = 2

When n= 2 , we get (a₁ +a₂)

Hence

a₁ +a₂= 4 + 2 = 6

Hence a₂= 4

Now if n= 3, we get (a1 +a₂ +a₃ )

Hence

a1 +a₂ +a₃ = 9+ 3 = 12

a₃ = 12-2-4 =6

Similarily we get a1 ,a2 ,a3 ,a4 ,a5 ,a6 ,......

now if we see

a₂ - a₁ = a₃ - a₂= a₄ - a₃ = 2= constant

HeHence we can say this forms an A.P.

sagar kumar

Last Activity: 7 Years ago

Use the formula tn= a+(n-1)d =n2+n+1(sorry n2= n square) . To get square term here lets assume d=n . So a+n2-n=n2+n+1. So we can solve for a and it comes up to be 2n+1.

So by using a=2n+1 and d=n we can get nth term as n2+n+1. This is not the only assumed values,there may be much more . So how could you say that it is not possible??

Shaikh Muzzakir

Last Activity: 7 Years ago

Sum of the nth number is n^2+n. ....givenT1=1+1=2. =A1.... ( 1 ) T2=4+2=6. =A1+A2. ( 2 ) A1+A2=6A2=4. From ( 1 )T3=9+3=12. = A1+A2+A3. ( 3 )A1+A2+A3=12A3=6. From( 2 )Hence, A2-A1=A3-A2=A4-A3 and so on...................The difference between them is d=2...........Therefore the given equation is A.P