A-LevelMathematicsSeries9709/12 · Feb/Mar 2024 · Q88 Marks
An arithmetic progression is such that its first term is 6 and its tenth term is 19.5. Find the sum of the first 100 terms of this arithmetic progression.
- (a)An arithmetic progression is such that its first term is 6 and its tenth term is 19.5. Find the sum of the first 100 terms of this arithmetic progression.[4]
- (b)A geometric progression a₁, a₂, a₃, … is such that a₁ = 24 and the common ratio is 1/2. The sum to infinity of this geometric progression is denoted by S. The sum to infinity of the even-numbered terms (i.e. a₂, a₄, a₆, …) is denoted by S_(E). Find the values of S and S_(E).[4]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.
- [*M1] Substitute n=10 and a=6 into uₙ = a + (n-1)d Expect 6+9d=19.5 or equivalent.
- [A1] [d =]1.5
- [DM1] Substitute a=6 and their d into correct formula for the sum of 100 terms
- [A1] Obtain 8025
- [B1] Obtain S=48
- [B1] Identify for SE first term 12 and common ratio ½
- [M1] Attempt sum to infinity, SE, with at least one of first term and common ratio correct Only awarded if |r| < 1.
- [A1] Obtain SE = 16
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