Theory question 109
Sequences and Series(a) The 3rd and 6th terms of a geometric progression (G.P.) are 2 and 54 respectively. Find the (i) common ratio (ii) first term (iii) sum of the first ten terms, correct the nearest whole number.
(b) The ratio of the coefficient of x4 to that of x3 in the binomial expansion of (1 + 2x)n is 3 : 1. Find the value of n.
Show the model answer
Model answer
(a)(i) ar2 = 2, ar5 = 54, so r3 = 27 and r = 3
(ii) a = 2/9
(iii) S10 = (2/9)(310 − 1)/(3 − 1) = 59048/9 ≈ 6561
(b) nC4(16) : nC3(8) = 3 : 1
2(n − 3)/4 = 3, so n − 3 = 6 and n = 9
Explanation
Divide the two GP terms to find r; for (b) use ⁿC₄/ⁿC₃ = (n − 3)/4.