Theory question 112
Sequences and Series(a) (i) Find the sum of the series A(1 + r) + A(1 + r)2 + ... + A(1 + r)n.
(ii) Given that r = 8% and A = GH¢40.00, find the sum of the 6th to 10th terms of the series in 12a(i).
(b) Find the equation of the tangent to the curve y = 1/x at the point on the curve, when x = 2.
Show the model answer
Model answer
(a)(i) G.P. with first term A(1 + r) and common ratio (1 + r)
Sn = A(1 + r)[(1 + r)n − 1]/r
(ii) Sum of T6 to T10 = S10 − S5 = 40(1.08)[(1.08)10 − (1.08)5]/0.08
= 540(2.15892 − 1.46933) ≈ GH¢372.38
(b) y = 1/2 at x = 2; dy/dx = −1/x2 = −1/4
y − ½ = −¼(x − 2)
x + 4y − 4 = 0
Explanation
The common ratio is 1 + r, so the sum formula divides by (1 + r) − 1 = r.