A-LevelMathematicsSeries9709/12 · Feb/Mar 2019 · Q67 Marks
The first and second terms of a geometric progression are p and 2p respectively, where p is a positive constant. The sum of the first n terms is greater than 1000p. Show that 2ⁿ > 1001.
- (i)The first and second terms of a geometric progression are p and 2p respectively, where p is a positive constant. The sum of the first n terms is greater than 1000p. Show that 2ⁿ > 1001.[2]
- (ii)In another case, p and 2p are the first and second terms respectively of an arithmetic progression. The nth term is 336 and the sum of the first n terms is 7224. Write down two equations in n and p and hence find the values of n and p.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] S_n = p(2ⁿ-1) / (2-1) soi
- [A1] p(2ⁿ-1)>1000p → 2ⁿ >1001
- [B1] p+(n-1)p=336
- [B1] n/2[2p+(n-1)p] = 7224
- [M1] Eliminate n or p to an equation in one variable
- [A1A1] n = 42, p = 8
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