Question

IF THE Nth term of a progression be a linear expression in N term prove that this progression is an AP

Answer 1

HOLA

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Let Nth term be given as

Tn = (an + b) ( Where A and B are constant)

Tn - 1 = a (n - 1) + b = { (an + b) - a}

So by subtracting them we have,

Tn - Tn - 1 = { (an + b) - (an + b) - a} = a

Hence the given is an progression

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HOPE U UNDERSTAND

Answer 2

ANSWER

Let the progression be tn

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According to the question: tn=an+b

Let us take the consecutive difference: tn−tn−1 =an+b−a(n−1)−b=2a

As the consecutive difference is constant, the sequence is an AP by definition of an AP.