An arithmetic sequence has first term a a\,a and common difference ddd. The sum of the first 25 terms of the sequence is equal to the square of the sum of the first 10 terms.
Show that 4a2+36ad+81d2=a+12d4a^2 + 36ad + 81d^2 = a + 12d4a2+36ad+81d2=a+12d.
Given that the possible values of a a\,a are -4 and −13\displaystyle -\frac{1}{3}−31, find the possible values of the 10th term of the sequence.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, 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. Each one has a worked solution and a mark scheme showing where the marks go.