If 2nd, 3rd and 6th terms of an A.P. are the three consecutive terms of a G.P., then the common ratio of the G.P. is : 1. 2 2. 3 3. 4.

Question

KnowledgeBoat · Accepted Answer

Let first term of A.P. be a and common difference be d. 2nd Term : a + d 3rd Term : a + 2d 6th Term : a + 5d These three terms form three consecutive terms of a G.P. Thus, a + d, a + 2d, a + 5d, ........ is the G.P. In G.P., ratio between consecutive terms are equal. ⇒ (a + 2d)2 = (a + d)(a + 5d) ⇒ a2 + 4ad + 4d2 = a2 + 5ad + ad + 5d2 ⇒ a2 + 4ad + 4d2 = a2 + 6ad + 5d2 ⇒ 0 = a2 - a2 + 6ad - 4ad + 5d2 - 4d2 ⇒ 0 = 2ad + d2 ⇒ d(2a + d) = 0 ⇒ d = 0 or 2a + d = 0 d cannot be equal to zero as then common ratio will be equal to 1, also not in options. ⇒ 2a + d = 0 ⇒ d = -2a Substitute d = −2a : a + d = a - 2a = -a a + 2d = a + 2(-2a) = -3a a + 5d = a + 5(-2a) = -9a r = = 3. Hence, option 2 is the correct option.

Mathematics

If 2nd, 3rd and 6th terms of an A.P. are the three consecutive terms of a G.P., then the common ratio of the G.P. is : 1. 2 2. 3 3. 4.

G.P.

Related Questions

If the 5th term of a G.P. is 2, then the product of its first nine terms is :
256
1024
512
2048

Mathematics

If 2nd, 3rd and 6th terms of an A.P. are the three consecutive terms of a G.P., then the common ratio of the G.P. is : 1. 2 2. 3 3. 4.

G.P.

Related Questions

If the 5th term of a G.P. is 2, then the product of its first nine terms is :25610245122048

If the 5th term of a G.P. is 2, then the product of its first nine terms is :
256
1024
512
2048