A-LevelMathematicsSeries9709/12 · Oct/Nov 2009 · Q36 Marks
A progression has a second term of 96 and a fourth term of 54. Find the first term of the progression in each of the following cases:
- (i)the progression is arithmetic,[3]
- (ii)the progression is geometric with a positive common ratio.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2009). The mark or mark type is shown in brackets.
- [1] a + d = 96 and a + 3d = 54 (B1)
- [2] d = -21, a = 117 (M1A1)
- [1] ar = 96 and ar³ = 54 (B1)
- [1] r² = 54/96 -> r = 3/4 (M1)
- [1] a = 128 (A1)
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