Answer:
179:321
Step-by-step explanation:
If Sn is the sum of the first n term of a sequence, the ratio will be expressed as:
Sn/S'n = 5n+4/9n+6
The sum of nth term of a sequence is expressed as
Sn = n/2[2a+(n-1)d]
The expression becomes
{n/2[2a+(n-1)d]}/{n/2[2a+(n-1)d']} = 5n+4/9n+4
Open the bracket
a+(n-1/2)d/a+(n-1/2)d' = 5n+4/9n+4
Since the 18th tern is expressed as
T18 = a+(18-1)d
T18 = a+17d
The expression becomes
T18/T'18 = a+(n-1/2)d/a+(n-1/2)d'
a+17d/a'+17d' = a+(n-1/2)d/a+(n-1/2)d'
Compare and contrast to get n
On comparing both sides of the equation
17 = n-1/2
n-1 = 17×2
n-1 = 34
n = 34+1
n = 35
If the nth term is 5n+4
18th term will be 5(35)+4 = 179
If the nth term is 9n+6
18th term will be 9(35)+6= 321
Hence the ratio of their 18th term will be 179:321
