(a) A geometric progression is such that the second term is equal to 24% of the sum to infinity. Find the possible values of the common ratio. [3]

(b) An arithmetic progression P has first term a and common difference d. An arithmetic progression Q has first term \(2(a+1)\) and common difference \(d+1\). It is given that \[\frac{\text{5th term of P}}{\text{12th term of Q}}=\frac13,\qquad\frac{\text{sum of first 5 terms of P}}{\text{sum of first 5 terms of Q}}=\frac23.\]

(b) Find the value of a and the value of d. [6]