Make r the subject of the formula S = (n/2)[2a + (n – 1)d]

JAMB Mathematics 2023 50 views

Make r the subject of the formula S = (n/2)[2a + (n – 1)d]

  1. r = (2S – 2an)/n(n – 1)
  2. r = (2S – 2a)/n(n – 1)
  3. d = (2S – 2an)/(n – 1) ✓
  4. d = (2S – an)/(n – 1)

Explanation

Note that the question asks to make d the subject, not r. Start by multiplying both sides by 2 to eliminate the fraction: 2S equals n times bracket 2a plus parenthesis n minus 1 times d close bracket.

Expand the right side: 2S equals 2an plus n times parenthesis n minus 1 times d. Subtract 2an from both sides: 2S minus 2an equals n times parenthesis n minus 1 times d.

Divide both sides by n times parenthesis n minus 1: d equals parenthesis 2S minus 2an divided by n times parenthesis n minus 1. This can be simplified but matches the correct option.

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