Question

answer please
question 23

Answer 1

In the first AP:
a = a
d = d

In 2nd AP:
a = A
d = D

Sn = n/2 [2a + (n-1)d]

4n+1 / 4n+27 = [(n/2){2a + (n-1)d}]/[(n/2){2A + (n-1)D}

In RHS , n & n cancels out (multiply the 1/2 inside the bracket)

4n+1/4n+27 = [a + {(n-1)/2}d]/[A + {(n-1)/2}D]

For getting 9th term, (n-1)/2 = 8 (since Tn = a + (n-1)d)
==> n-1 = 16
==> n = 17

Substituting n=17 in LHS

4n+1/4n+27
= 4(17)+1/4(17)+27
= 69 / 95

Hence the ratio of their 9th term is 69:95

Hope this helps!