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.
Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 156 questions covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
