Pearson Edexcel IAL Mathematics P2.4.2 Arithmetic sequences & series

Practise finding terms, sums, common differences and thresholds in arithmetic sequences, including savings schemes and linear growth models.

[Maximum number: 7]

In a large theatre there are n rows of seats, where n is a constant.

The number of seats in the first row is a, where a is a constant.
In each subsequent row there are 4 more seats than in the previous row so that
- in the 2 nd row there are (a+4) seats
- in the 3 rd row there are (a+8) seats
- the number of seats in each row form an arithmetic sequence

Given that the total number of seats in the first 10 rows is 360

(a)

find the value of a.

Given also that the total number of seats in the n rows is 2146

[ 2 ]

M1: Uses $S_{10}=360$ with a correct formula to set up a linear equation in " a ". E.g. $\frac{10}{2}\{2 \times a+9 \times 4\}=360$ Alternatively uses the sum of all 10 terms

a+(a+4)+(a+8)+(a+12)+(a+16)+(a+20)+(a+24)+(a+28)+(a+32)+(a+36)=360

A1: a=18 following a correct equation

(b)

show that

n^{2}+8 n-1073=0

[ 2 ]

$S_n=2146$ $\frac{n}{2}\{2(18)+(n-1)4\}=2146$ $n^2+8n-1073=0$

M1
A1*

(c)

Hence

[ 3 ]

(i)

state the number of rows of seats in the theatre,

[ 1 ]

(ii)

find the maximum number of seats in any one row.

[ 2 ]

$18+(29-1)\times4=130$
Maximum number of seats =130.

M1
A1

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P2.4.2 - Arithmetic sequences and series question 1

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)