Theory question 111
Binomial Theorem(a)(i) Write down the Binomial expansion of (1 + x)4. (ii) Use the result in 11(a)(i) to evaluate, correct to three decimal places (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 its common difference.
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Model answer
(a)(i) 1 + 4x + 6x² + 4x³ + x⁴.
(ii) x = ¼: 1 + 1 + 0.375 + 0.0625 + 0.0039 ≈ 2.441.
(b) (7 + d)² = 7(7 + 4d) gives d² = 14d, so d = 14 (d ≠ 0).
Explanation
For G.P. terms, (middle)² = first × third.