## msingh 2 years ago Can anyone derive me the formula for the nth term from the Last , of A.P?

1. ash2326

You want to derive the formula for the nth term of an A.P?

2. msingh

kk..

3. ash2326

Let the first term be a1 and the common difference be d now second term will be a2=a1+d third term will be a3=a1+d+d=a1+2d Do you get this part?

4. msingh

yes..

5. ash2326

Now if we go on like that, 4th term is \[a_4=a_1+3d\] Hence nth term will be \[a_n=a_1+(n-1)d\] Do you understand this?

6. msingh

yes..and thank u

7. msingh

one question..why do we add 1 on last step

8. msingh

because thee are n terms and before we have n-1 terms

9. msingh

it goes on decreasing such as n, n-1, n-2...

10. ash2326

I don't get you, where do you have doubt?

11. msingh

an=a1+(n−1)d, y there is 1

12. ash2326

you mean the 1 in n-1?

13. msingh

yes.

14. ash2326

for seond term a2, we have d or 1d for third term a3, we have 2 d In the formula we have d times ( one no. less than the term no. ) That's why for n we have 1 less than n i.e n-1

15. msingh

kkk

16. ash2326

Do you understand?

17. msingh

yes