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A sequence 192, 360, 576……. is formed by multiplying the corresponding terms of two different Arithmetic Progressions. What is the eighth term of the sequence?
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A
2376
💡 Explanation:
Let AP1 be: a, a+d, a+2d, ... and AP2 be: b, b+e, b+2e, ... The product sequence is: ab, (a+d)(b+e), (a+2d)(b+2e), ... Term 1: 192 = ab, Term 2: 360 = (a+d)(b+e) = ab + ae + bd + de, Term 3: 576 = (a+2d)(b+2e). From 192 to 360, difference is 168. From 360 to 576, difference is 216. The second difference is 216-168=48. For product of two APs, the 8th term follows the pattern. Through calculation: if we factor 192 = 12×16, 360 = 15×24, 576 = 18×32, then AP1: 12, 15, 18, 21, 24, 27, 30, 33 and AP2: 16, 24, 32, 40, 48, 56, 64, 72. Term 8 = 33 × 72 = 2376.