4 th term of an A.P. is equal to 3 times its first term and 7 th term exceeds twice the 3 rd term by 1. Find the first term and the common difference.

Let first term be a and common difference be d. According to question, ⇒ a 4 = 3a ⇒ a + (4 - 1)d = 3(a) ⇒ a + 3d = 3a ⇒ 2a = 3d ⇒ a = ........(i) Also, ⇒ a 7 - 2a 3 = 1 ⇒ a + (7 - 1)d - 2[a + (3 - 1)d] = 1 ⇒ a + 6d - 2(a + 2d) = 1 ⇒ a + 6d - 2a - 4d = 1 ⇒ a - 2a + 2d = 1 ⇒ -a + 2d = 1 Substituting value of a from (i) in above equation, Substituting value of d in (i) we get, a = = 3. Hence, first term = 3 and common difference = 2.

State, true or false: if a, b and c are in A.P. then :
(i) 4a, 4b and 4c are in A.P.
(ii) a + 4, b + 4 and c + 4 are in A.P.

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An A.P. consists of 57 terms of which 7^th term is 13 and the last term is 108. Find the 45^th term of this A.P.

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The sum of the 2^nd term and the 7^th term of an A.P. is 30. If its 15^th term is 1 less than twice of its 8^th term, find the A.P.

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In an A.P. if m^th term is n and n^th term is m, show that its r^th term is (m + n - r).

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Mathematics

4^th term of an A.P. is equal to 3 times its first term and 7^th term exceeds twice the 3^rd term by 1. Find the first term and the common difference.

AP

Related Questions

State, true or false: if a, b and c are in A.P. then :
(i) 4a, 4b and 4c are in A.P.
(ii) a + 4, b + 4 and c + 4 are in A.P.

An A.P. consists of 57 terms of which 7^th term is 13 and the last term is 108. Find the 45^th term of this A.P.

The sum of the 2^nd term and the 7^th term of an A.P. is 30. If its 15^th term is 1 less than twice of its 8^th term, find the A.P.

In an A.P. if m^th term is n and n^th term is m, show that its r^th term is (m + n - r).

Mathematics

4th term of an A.P. is equal to 3 times its first term and 7th term exceeds twice the 3rd term by 1. Find the first term and the common difference.

AP

Related Questions

State, true or false: if a, b and c are in A.P. then :(i) 4a, 4b and 4c are in A.P.(ii) a + 4, b + 4 and c + 4 are in A.P.

An A.P. consists of 57 terms of which 7th term is 13 and the last term is 108. Find the 45th term of this A.P.

The sum of the 2nd term and the 7th term of an A.P. is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P.

In an A.P. if mth term is n and nth term is m, show that its rth term is (m + n - r).

4^th term of an A.P. is equal to 3 times its first term and 7^th term exceeds twice the 3^rd term by 1. Find the first term and the common difference.

State, true or false: if a, b and c are in A.P. then :
(i) 4a, 4b and 4c are in A.P.
(ii) a + 4, b + 4 and c + 4 are in A.P.

An A.P. consists of 57 terms of which 7^th term is 13 and the last term is 108. Find the 45^th term of this A.P.

The sum of the 2^nd term and the 7^th term of an A.P. is 30. If its 15^th term is 1 less than twice of its 8^th term, find the A.P.

In an A.P. if m^th term is n and n^th term is m, show that its r^th term is (m + n - r).