msingh
Can anyone derive me the formula for the nth term from the Last , of A.P?
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ash2326
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You want to derive the formula for the nth term of an A.P?
msingh
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kk..
ash2326
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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?
msingh
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yes..
ash2326
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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?
msingh
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yes..and thank u
msingh
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one question..why do we add 1 on last step
msingh
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because thee are n terms and before we have n-1 terms
msingh
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it goes on decreasing such as n, n-1, n-2...
ash2326
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I don't get you, where do you have doubt?
msingh
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an=a1+(n−1)d, y there is 1
ash2326
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you mean the 1 in n-1?
msingh
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yes.
ash2326
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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
msingh
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kkk
ash2326
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Do you understand?
msingh
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yes