Question

the ratio of 2nd and 5th terms of an arithmetic sequence is 3:4 then what is the ratio of 5th and 9th terms

Answer 1

Answer:

let the 1st term is a

common difference d

2nd term=a+(2-1).d=a+d

5th term=a+(5-1).d=a+4d

so,

(a+d) : (a+4d)=3 : 4

=> (a+d)/(a+4d)=3/4

=> 4(a+d)=3(a+4d)

=> 4a+4d=3a+12d

=> 4a-3a=12d-4d

=> a=8d

now the ratio of 5th and 9th term

{a+(5-1).d} : {a+(9-1).d

=(a+4d)/(a+8d)

putting the value of a=8d

(8d+4d)/(8d+8d)

=12d/16d

=12/16

=3/4

so ratio of 5th term and 9th term is 3 : 4