How many arithmetic progressions with 10 terms are there whose first term in the set {1, 2, 3} and whose common difference is in the set {2, 3, 4}?

Question

Philoid · Accepted Answer

Given: Two sets: {1, 2, 3} & {2, 3, 4}

To find: number of A.P. with 10n terms whose first term is in the set {1, 2, 3} and whose common difference is in the set {2, 3, 4}

Number of arithmetic progressions with 10 terms whose first term are in the set {1, 2, 3} and whose common difference is in the set {2, 3, 4} are:3 × 3=9

(3 because there are three elements in the set {1, 2, 3} and another 3 because there are three elements in the set {2, 3, 4})