20N.1.SL.TZ0.T_15

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

Mia baked a very large apple pie that she cuts into slices to share with her friends. The smallest slice is cut first. The volume of each successive slice of pie forms a geometric sequence.

The second smallest slice has a volume of $30 {cm}^{3}$ . The fifth smallest slice has a volume of $240 {cm}^{3}$ .

Find the common ratio of the sequence.

[2]

Find the volume of the smallest slice of pie.

[2]

The apple pie has a volume of $61 425 {cm}^{3}$ .

Find the total number of slices Mia can cut from this pie.

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure. It appeared in a paper that permitted the use of a calculator, and so might not be suitable for all forms of practice.

$u_{1} r = 30$ and $u_{1} r^{4} = 240,$ (M1)

Note: Award (M1) for both the given terms expressed in the formula for $u_{n}$ .

OR

$30 r^{3} = 240 (r^{3} = 8)$ (M1)

Note: Award (M1) for a correct equation seen.

$(r =) 2$ (A1) (C2)

[2 marks]

$u_{1} \times 2 = 30$ OR $u_{1} \times 2^{4} = 240$ (M1)

Note: Award (M1) for their correct substitution in geometric sequence formula.

$(u_{1} =) 15$ (A1)(ft) (C2)

Note: Follow through from part (a).

[2 marks]

$\frac{15 (2^{n} - 1)}{2 - 1} = 61425$ (M1)

Note: Award (M1) for correctly substituted geometric series formula equated to $61425$ .

$(n =) 12$ (slices) (A1)(ft) (C2)

Note: Follow through from parts (a) and (b).

[2 marks]

Examiners’ report

[N/A]