Prove that no matters what the real numbers A and B are the pattern of number but an A+ nb is always an a.p. what is the common difference what's the sum of first 20 terms
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nth term, an=a+nb n-1 th term, an-1=a+(n-1)b
Difference of two consecutive terms = an-an-1= a+nb-a-nb+b = b
which is constant
Hence the sequence is an AP and the common difference is b
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