21M.2.SL.TZ2.3

pestleMathematicsAASLPaper 221M· sl-1-2-arithmetic-sequences-and-seriessource ↗

An arithmetic sequence has first term $60$ and common difference $- 2.5$ .

Given that the $k$ th term of the sequence is zero, find the value of $k$ .

[2]

Let $S_{n}$ denote the sum of the first $n$ terms of the sequence.

Find the maximum value of $S_{n}$ .

[3]

Markscheme / solution

attempt to use $u_{1} + (n - 1) d = 0$ (M1)

$60 - 2.5 (k - 1) = 0$

$k = 25$ A1

[2 marks]

METHOD 1

attempting to express $S_{n}$ in terms of $n$ (M1)

use of a graph or a table to attempt to find the maximum sum (M1)

$= 750$ A1

METHOD 2

EITHER

recognizing maximum occurs at $n = 25$ (M1)

$S_{25} = \frac{25}{2} (60 + 0), S_{25} = \frac{25}{2} (2 \times 60 + 24 \times - 2.5)$ (A1)

attempting to calculate $S_{24}$ (M1)

$S_{24} = \frac{24}{2} (2 \times 60 + 23 \times - 2.5)$ (A1)

THEN

$= 750$ A1

[3 marks]

Examiners’ report

[N/A]