A-LevelMathematicsSeries9709/12 · Oct/Nov 2010 · Q56 Marks
The first and second terms of an arithmetic progression are 161 and 154 respectively. The sum of the first m terms is zero. Find the value of m.
- (a)The first and second terms of an arithmetic progression are 161 and 154 respectively. The sum of the first m terms is zero. Find the value of m.[3]
- (b)A geometric progression, in which all the terms are positive, has common ratio r. The sum of the first n terms is less than 90% of the sum to infinity. Show that rⁿ > 0.1.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- [B1] d= -7 used co
- [M1] (m/2)[322 + (m - 1)(-7)] = 0 Condone omission of (m/2). Statement co (condone m = 0)
- [A1] 47 co (condone m = 0)
- [M1] a(1-rⁿ)/(1-r) < 0.9a/(1-r) Allow for =, <, >, ≤, ≥
- [M1] 1-rⁿ < 0.9 Needs inequality sign correct
- [A1] rⁿ > 0.1 co
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