In a sustainable construction project, the number of solar panels installed during each of the first three months is represented by the following expressions:
4k−1,7k−5,12k−19 4k - 1, \quad 7k - 5, \quad 12k - 19 4k−1,7k−5,12k−19Show that k=5k = 5k=5 is the unique value for which these monthly installation figures form an arithmetic sequence.
State the number of panels installed in the first month.
Determine the common difference for this sequence.
The total number of solar panels installed after NNN months is given by SNS_NSN.
Given that
SN<25 000 S_N < 25\,000 SN<25000 SN+1>25 000 S_{N+1} > 25\,000 SN+1>25000Find the value of NNN.
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.