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Can anyone derive me the formula for the nth term from the Last , of A.P?

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

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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?
yes..and thank u
one question..why do we add 1 on last step
because thee are n terms and before we have n-1 terms
it goes on decreasing such as n, n-1, n-2...
I don't get you, where do you have doubt?
an=a1+(n−1)d, y there is 1
you mean the 1 in n-1?
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
Do you understand?

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