If the nth terms of the two AP’s 9, 7, 5, … and 24, 21, 18 … are the same, then find the value of n. Also, that term.
First term of first AP, a = 9
First term of second AP, A = 24
Common difference of first AP, d = 7 - 9 = - 2
Common difference of second AP, D = 21 - 24 = - 3
Given that nth term is same i.e
An = an
As we know, nth term of an AP is
an = a + (n - 1)d
where a = first term
an is nth term
d is the common difference
A + (n - 1)D = a + (n - 1)d
24 + (n - 1) (- 3) = 9 + (n - 1) (- 2)
24 - 3n + 3 = 9 - 2n + 2
27 - 3n = 11 - 2n
3n - 2n = 27 - 11
n = 16
i.e their 16th term is equal in both cases,
and a16 = A16 = a + 15d = 9 + 15 (- 2) = - 21