Mathematics

Problem

Both an A.P. and a G.P. begin with the same first term

4

. Their respectively unknown common difference

d

and common ratio

r

(

r>0

r\neq 1

) satisfy the following conditions: • The

m

-th term of the A.P. equals the

n

-th term of the G.P. • The

(m+3)

-rd term of the A.P. equals the

(n+1)

-th term of the G.P. a. (i) Express

d

in terms of

r

m

and

n

. b. (ii) Hence find the numerical values of

d

and

r

when

m=5

and

n=3