Theory question 112
Progressions(a) The eighth term of an Arithmetic Progression (A.P) is 46 and the sum of the first eight terms is 200. Find the: (i) first term; (ii) sum of the first 12 terms.
(b) The points X(70°S, 60°E) and Y(7°S, 60°E) lie on the surface of the earth. (i) Illustrate the information in a diagram. (ii) Find the distance between X and Y along the meridian. [Take π = 22/7 and R = 6,400 km]
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Model answer
(a) a + 7d = 46; S8 = 4(2a + 7d) = 200 ⇒ 2a + 7d = 50 ⇒ a = 4, d = 6
(i) First term = 4
(ii) S12 = 6(2 × 4 + 11 × 6) = 6 × 74 = 444
(b)(i) Sketch the earth with the equator and the meridian 60°E; mark Y at 7°S and X at 70°S on it
(ii) Angle between them = 70° − 7° = 63°; distance = 63/360 × 2 × 22/7 × 6400 = 7,040 km
Explanation
Both points are south, so subtract the latitudes.