The nth term represents any specific position in an arithmetic progression. It’s found by adding the common difference multiplied by one less than position number to first term. For example: to find 5th term add common difference multiplied by 4 to first term.
A sequence of numbers where each term differs from the previous term by a constant value (common difference) forms an arithmetic progression. The constant difference between consecutive terms is denoted by ‘d’. The first term is represented as ‘a’. The sequence can extend infinitely in both directions and follows predictable patterns.
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Let’s derive aₘ₊ₙ in an AP:
Given:
– First term = a₁
– Common difference = d
– General term aₙ = a₁ + (n-1)d
For term aₘ₊ₙ:
aₘ₊ₙ = a₁ + (m+n-1)d
This is not equal to:
– aₘ + aₙ = [a₁ + (m-1)d] + [a₁ + (n-1)d]
– aₘ × aₙ = [a₁ + (m-1)d] × [a₁ + (n-1)d]
– aₘ – aₙ = [a₁ + (m-1)d] – [a₁ + (n-1)d]
Therefore aₘ₊ₙ is not equal to any of the given options:
aₘ + aₙ or aₘ × aₙ or aₘ – aₙ
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