Question

If the nth term of a progression be a linear equation in n,prove that this progression is an A.P.
plz answer ASAP

Answer 1

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$<b>Given = nth term of AP is in linear expression in n. Let the two variables be a and b So, nth term = an + b => an = an + b For 1st term, a1 = a + b For 2nd term a2 = 2a + b For 3rd term a3 = 3a + b and so on.... Now, for a sequence of numbers to be an AP, there must be a common difference. So, to satisfy the condition of AP, a3 - a2 = a2 - a1 = d (common difference) => (3a + b) - (2a + b) = (2a + b) - (a + b) => a = a Since d = a, this sequence or progression is an AP.$

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