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1.6 Sequences and Series

1.6 Sequences and Series

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Question 141

A vertical farm designs its irrigation system based on the number of seedling trays in each tier. The number of trays in the first three tiers is given by the expressions:

2k+5,4k−2,8k−23 2k + 5, \quad 4k - 2, \quad 8k - 23 2k+5,4k−2,8k−23
a.

Show that k=7k = 7k=7 is the only value for which these expressions form an arithmetic sequence.

[3]
bi.

Write down the number of trays in the first tier.

[1]
bii.

Determine the common difference of the sequence representing the number of trays per tier.

[1]
c.

The total number of trays in the first NNN tiers is denoted by SNS_NSN​. Given that

SN<80 000 S_N < 80\,000 SN​<80000 SN+1>80 000 S_{N+1} > 80\,000 SN+1​>80000

find the value of NNN.

[4]
Markscheme

1.6 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.6 Sequences and Series

308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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