O-LevelAdditional MathematicsSeries4037/22 · May/June 2025 · Q79 Marks
The first three terms of an arithmetic progression can be written as 2ln(x³), 51n(x²), 2ln(x⁷).
- (a)Given that x > 1, find the least number of terms for the sum of this progression to be greater than 43 ln (x²⁴).[6]
- (b)Given that the 25th term of this progression is equal to 408, find the exact value of x.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [M2] Forms a correct inequality/equation from which the logarithms can be eliminated, e.g. n/2(12lnx+(n-1)×4lnx) > 43×24lnx oe, soi (M2 for a=6 and d=4 or a=6lnx soi and d=4lnx soi or a=lnx6 soi and d=2/3lnx6 soi)
- [A1] 2n²+4n-1032[*0]oe
- [M1] Solves their 3-term quadratic in n
- [A1] n = 22 cao, nfww
- [B1] Correct expression for the 25th term, e.g. 6lnx+24×4lnx or 102lnx soi
- [M1] Forms and correctly simplifies an equation e.g. 102 lnx = 408
- [A1] x = e4
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →