There are two AP with different first term and common difference.
For the First AP
Let first term be a
Common difference = d
Sum of n terms =
and nth term = an = a + (n – 1)d
For the second AP
Let first term be A
Common difference = D
Sum of n terms =
and nth term = An = A + (n – 1)D
It is given that
Now, we need to find ratio of their 18th term
n – 1 = 17 × 2
⇒ n = 34 + 1
⇒ n = 35
Putting n = 35 in eq. (i), we get
Hence the ratio of 18th term of 1st AP and 18th term if 2nd AP is 179:321