A-LevelMathematicsSeries9709/12 · Oct/Nov 2012 · Q89 Marks
In a geometric progression, all the terms are positive, the second term is 24 and the fourth term is 13½. Find the first term,
- (a)(i)In a geometric progression, all the terms are positive, the second term is 24 and the fourth term is 13½. Find the first term,[3]
- (a)(ii)the sum to infinity of the progression.[2]
- (b)A circle is divided into n sectors in such a way that the angles of the sectors are in arithmetic progression. The smallest two angles are 3° and 5°. Find the value of n.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.
- [B1] ar = 24, ar³ = 13½ (Both needed)
- [M1] Eliminates a (or r) to find r = ¾ (Method of Solution.)
- [A1] → a = 32
- [M1] sum to infinity = a / (1 - r) (Correct formula used.)
- [A1] = 128
- [B1] a = 3, d = 2 (Correct values for first term and common difference)
- [M1] Sₙ = n/2(2a + (n-1)d) (= 360) (Correct Sₙ used.)
- [M1] → 2n² + 4n - 720 = 0 (Correct quadratic)
- [A1] → n = 18
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