O-LevelAdditional MathematicsSeries4037/22 · Oct/Nov 2020 · Q78 Marks
A geometric progression has a first term of 3 and a second term of 2.4. For this progression, find
- (a)the sum of the first 8 terms,[3]
- (b)the sum to infinity,[1]
- (c)the least number of terms for which the sum is greater than 95% of the sum to infinity.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [B1] (a) a=3 r=2.4/3 = 0.8
- [M1] (a) S₈ = 3(1-0.8⁸) / (1-0.8) Inserts their a and r into S₈
- [A1] (a) = 12.48 awrt or 12.5
- [B1] (b) S_∞ = 3 / (1-0.8) = 15
- [M1] (c) S_n = 15(1 – 0.8^n) > 0.95 × 15 their correctly produced S_n > 0.95S_∞
- [A1] (c) 0.8^n < 0.05 oe
- [M1] (c) n < log 0.05 / log 0.8 Dep takes logs correctly of their expression with power of n.
- [A1] (c) n = 14 nfww
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