Question

Two APS have the same first and last terms.The first AP has 21 terms with a common differences of 9. How many terms has the other ap if its common differences is 4.

Answer 1

first AS:
first term: a
d = 9
n = 21
term(21) = a + 9(20) = a + 180

2nd AS
first term : a
d = 4
term(n) = a + 4(n-1)

a + 4(n-1) = a + 180
4n - 4 = 180
4n = 184
n = 46 <----- number of terms for the 2nd sequence

check
term(21) for the first = a + 180
term(46) for the second = a + 4(45) = a + 180 , the same as the last term of sequence #1
looks like the first term could be anything, as long as it is the same for both