Question

Two APs are given 9, 7, 5...... and 24,21,18... If nth term of both the progressions are equal then find the value of n and nth term.
The answer is 16,-21.
Please solve this with proper steps.

Answer 1

a+(n-1)d=a₁+(n₁-1)d₁

9+(n-1)-2=24+(n-1)-3

9-2n+2=24-3n+3

n=16


$a_{n} =$a+(n-1)d

=9-30

=-21