If the ratio of the sum of first n terms of two A.Ps is (7n+1):(4n+27). Then find the ratio of their 9th term.
Answers
Answered by
6
Sn =n/2 {a1 + (n - 1)d1}
Sn' = n/2 { a2 + (n - 1) d2}
a1 + (n - 1) d1 / a2 + (n - 1) d2 = 7n + 1 / 4n + 27
In order to find nth term, we have to replace n by 2m - 1
a1 + (2m - 1) d1 / a2 +(2m -1)/ d2
= 7(2m - 1) + 1/ 4(2m -1) + 27
= 14m - 7 + 1/ 8m - 4+27
= 14m - 6/ 8m + 23
Now replace m by 9 to get the ratio of 9th term
= 14(9) - 6/ 8(9) + 23
= 120/95
= 24/19
Sn' = n/2 { a2 + (n - 1) d2}
a1 + (n - 1) d1 / a2 + (n - 1) d2 = 7n + 1 / 4n + 27
In order to find nth term, we have to replace n by 2m - 1
a1 + (2m - 1) d1 / a2 +(2m -1)/ d2
= 7(2m - 1) + 1/ 4(2m -1) + 27
= 14m - 7 + 1/ 8m - 4+27
= 14m - 6/ 8m + 23
Now replace m by 9 to get the ratio of 9th term
= 14(9) - 6/ 8(9) + 23
= 120/95
= 24/19
Similar questions