1.10: Related arithmetic and geometric series

4PM1/2R/November/2020 — Question 1 · 6 marks

The n\displaystyle nth term of an arithmetic series A\displaystyle A is an\displaystyle a_n. The n\displaystyle nth term of a geometric series G\displaystyle G is tn\displaystyle t_n.
For these two series,
a1=t1,a10=t3=48,a10=4t2.a_1=t_1, \qquad a_{10}=t_3=48, \qquad a_{10}=4t_2.
Find
(i) the common ratio of G\displaystyle G,
(ii) the common difference of A\displaystyle A.
(6)