Theory question 101
Sequences and SeriesThe sum of the 2nd and 5th terms of an arithmetic progression (A.P) is 42. If the difference between the 6th and the 3rd terms is 12, find the (a) common difference; (b) first term; (c) 20th term.
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Model answer
T₂ + T₅ = (a + d) + (a + 4d) = 2a + 5d = 42
T₆ − T₃ = 3d = 12
(a) d = 4
(b) 2a + 20 = 42, so a = 11
(c) T₂₀ = a + 19d = 11 + 76 = 87
Explanation
Write each term as a + (n − 1)d and solve the two equations.