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Vikram writes the first term of an AP with first term a and common difference d as a + d, saying 'one step of d has been taken'. What is wrong with his reasoning?

Class 10nth Term of an APAlgebra — Sequences
  • ANothing is wrong; the first term really is a + d
  • BPutting n = 1 in a + (n - 1)d gives a + 0*d = a, so no step of d has been taken yet
  • CThe first term should be a - d, because one step must be undone
  • DThe formula a + (n - 1)d only works from the 2nd term onwards

Step-by-Step Solution

The nth term counts the steps taken AFTER the first term, so the first term has taken none: . Vikram's is the 2nd term. The formula is valid for every from 1 onwards - this off-by-one is the most common slip in AP work.
Answer: B) Putting n = 1 in a + (n - 1)d gives a + 0*d = a, so no step of d has been taken yet

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