Q1) Let k > 0
(a) (i) Find the common ratio of the GP k, 10k, 100k.
(ii) Finf the sum of the first n terms og GP k, 10k, 100k,…
(b) (i) Show that
log10 k, log10 10k, log10 100k
is an AP.
(ii) Find the sum of the first n terms of AP
log10 k, log10 10k, log10 100k,….
Also, if n = 10, what is the sum?
Q2) a and b are positive numbers a, -2, b form a GP and -2, b, a
form an AP.
(a) Find the value of ab.
(b) Find the values of a and b.
(c) (i) Find the sum to infinity of the GP a, -2, b,…
(ii)Find the sum to infinity of all the terms that are positive in the GP
a, -2, b,…
Q3) $P is deposited in a bank at the interst rate of r% per annum
compounded annually. At the end of each year, 1/3 of the amount in
the account (including principal and interest) is drawn out and the
remainder is redeposited at the same rate.
Let $Q1, $Q2, $Q3,… denote respectively the sums of money
drawn out at the end of the first year, second year, third year,….
a) (i) Express Q1 and Q2 in terms of P and r.
(ii) Show that Q3 = 4/27P(1+r%)^3.
b) Q1 , Q2 , Q3 , … form a GP.Find the common ratio in terms of r.
c) Suppose Q3=27/128P .
(i) Find the value of r .
(ii) If P = 10000 , find Q1 + Q2 + Q3 + … + Q10 .
(Give your answer correct to the nearest integer.)
