Let \(k, a_2, a_3\) be a geometric sequence with common ratio \(p \neq 1,\) and let \(k, b_2, b_3\) be a geometric sequence with common ratio \(r \neq 1.\) If\(a_3-b_3=3(a_2-b_2)\)and \(p \neq r,\) then find \(p + r.\)
a2 = kp a3 = kp2 b2 = kr b3 = kr2
a3 - b3 = 3(a2 - b2) ---> kp2 - kr2 = 3(kp - kr)
k(p2 - r2) = 3k(p - r)
k(p + r)(p - r) = 3k(p - r)
Cancel: p + r = 3
