Theory question 104
ProgressionsIf the sixth term of an Arithmetic Progression (A. P.) is 37 and the sum of the first six terms is 147, find the: (a) first term; (b) sum of the first fifteen terms.
Show the model answer
Model answer
a + 5d = 37 and S₆ = 3(2a + 5d) = 147 → 2a + 5d = 49
Subtract: a = 12, so d = 5
(a) First term = 12
(b) S₁₅ = 15/2 (2 × 12 + 14 × 5) = 15/2 × 94 = 705
Explanation
Use Sn = n/2 (2a + (n − 1)d).