Problem Solving

dodgeforgmat wrote:In an AP, if A times the Ath term is equal to B times the Bth term, what is (A+B)th term of the AP

1.A^2 - B^2
2.A-B
3. 1
4. 0
5. Cannot be determined

If a is the 1st term of an AP, d is the common difference, then the nth term of the sequence is given by:
a(n) = a + (n - 1)d

Ath term = a + (A - 1)d
Bth term = a + (B - 1)d
(A + B)th term = a + [(A + B) - 1]d

Now, A * {a + (A - 1)d} = B * {a + (B - 1)d}
Aa + A²d - Ad = Ba + B²d - Bd
(A - B)a + (A² - B²)d = (A - B)d
Dividing throughout by (A - B),
a + (A + B)d = d
or a + {(A + B) - 1} = 0, which implies that (A + B)th term is 0.

The correct answer is 4.