Theory question 103
Sequences and SeriesThe twenty-first term of an Arithmetic progression (AP) is 5½ and the sum of the first twenty-one terms is 94½. Find the: (a) first term; (b) common difference; (c) sum of the first thirty terms.
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Model answer
a + 20d = 5.5
S21 = (21/2)(2a + 20d) = 94.5, so a + 10d = 4.5
Subtract: 10d = 1
(a) a = 3.5
(b) d = 0.1
(c) S30 = 15(2 × 3.5 + 29 × 0.1) = 15 × 9.9 = 148.5
Explanation
S₂₁ = (21/2)(2a + 20d) simplifies to 21(a + 10d).