A-LevelMathematicsSeries9709/12 · Oct/Nov 2021 · Q56 Marks
The first, third and fifth terms of an arithmetic progression are 2 cos x, -6√3 sin x and 10 cos x respectively, where π/6 < x < π.
- (a)Find the exact value of x.[3]
- (b)Hence find the exact sum of the first 25 terms of the progression.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [*M1] OE. From the given terms, obtain 2 expressions relating to the common difference of the arithmetic progression, attempt to solve them simultaneously and achieve an equation just involving sinx and cosx.
- [DM1] For use of sinx/cosx = tanx
- [A1] x = 5π/6 only
- [B1 FT] d = 2cosx or d = 2cos(their x)
- [M1] Using the correct sum formula with 25/2, (25 – 1) and with a replaced by either 2(cos(their x)) or √3 and d replaced by either 2(cos(their x)) or ±° √3 .
- [A1] -325√3 Must be exact.
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