#### Mathematics

- The first term of a geometric series is √3 and the 2nd term is √3 - 1.
- For which values of a is the infinite geometric series 2(3a - 1) + 2(3a - 1)2 + ... convergent?
- The first term of a sequence is T1 = 2 and Tk + 1 = 1⁄2Tk for all k ≥ 1.
- A sequence is generated by the recursive formula T1 = 4 and Tk+1 = Tk + 3 for all k ≥ 1.
- 2, x and y are the first three terms of a an arithmetic sequence. If each term is decreased by 1, the resulting sequence is geometric. Find the two sequences.
- The sum of the first n terms of a certain sequence is Sn = n2 + 2n
- Determine the values of x and y so that the sequence -3⁄4; x; y; 2⁄9 is a geometric sequence.
- Find the sum of all the multiples of 3 between 1 and 400
- The first three terms of an arithmetic sequence are 2x - 4; x - 3 and 8 - 2x. Determine the value of x and hence the sum of the first 41 terms.
- Thnth term of a geometric sequence is 8 X 5n - 3.