20N.1.AHL.TZ0.H_5

pestleMathematicsAAHLPaper 120N· sl-1-3-geometric-sequences-and-seriessource ↗

The first term in an arithmetic sequence is $4$ and the fifth term is $\log_{2} 625$ .

Find the common difference of the sequence, expressing your answer in the form $\log_{2} p$ , where $p \in ℚ$ .

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$u_{5} = 4 + 4 d = \log_{2} 625$ (A1)

$4 d = \log_{2} 625 - 4$

attempt to write an integer (eg $4$ or $1$ ) in terms of $\log_{2}$ M1

$4 d = \log_{2} 625 - \log_{2} 16$

attempt to combine two logs into one M1

$4 d = \log_{2} (\frac{625}{16})$

$d = \frac{1}{4} \log_{2} (\frac{625}{16})$

attempt to use power rule for logs M1

$d = \log_{2} {(\frac{625}{16})}^{\frac{1}{4}}$

$d = \log_{2} (\frac{5}{2})$ A1

[5 marks]

Note: Award method marks in any order.

Examiners’ report

[N/A]