(a)(i) Write down the binomial expansion of \((1 + x)^{4}\). (ii) Use the result in (a)(i) to evaluate, correct to three decimal places \((\frac{5}{4})^{4}\...

(a)(i) Write down the binomial expansion of \((1 + x)^{4}\).

(ii) Use the result in (a)(i) to evaluate, correct to three decimal places \((\frac{5}{4})^{4}\).

(b) The first, second and fifth terms of a linear sequence (A.P) are three consecutive terms of an exponential sequence (G.P). If the first term of the linear sequence is 7, find the common difference.