An environmental group plants saplings in a reforestation zone. The number of saplings planted each week follows an arithmetic progression. In week 5, 38 saplings are planted. The total number of saplings planted across the first 12 weeks is S12=510S_{12} = 510S12=510. Determine the number of saplings planted in week 1 and the common difference of the progression.
In a second reforestation zone, saplings are also planted weekly in an arithmetic progression. In the first week, 86 saplings are planted, and the number of saplings planted decreases by 5 each week. The sum of the first nnn terms of this second progression is TnT_nTn. Let SnS_nSn be the sum of the first nnn terms of the first progression from part (a). Find the value of nnn such that Tn=SnT_n = S_nTn=Sn, where n>0n > 0n>0.
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.