18th term of an A.P. is equal to 4 times its 4th term and the 6th term exceeds twice the 2nd term by 4. Find the sum of the first 9 terms of this A.P.

Question

KnowledgeBoat · Accepted Answer

We know that, an = a + (n - 1)d Given, 18th term of an A.P. is equal to 4 times its 4th term a18 = a + 17d a4 = a + 3d ⇒ a + 17d = 4(a + 3d) ⇒ a + 17d = 4a + 12d ⇒ a - 4a + 17d - 12d = 0 ⇒ -3a + 5d = 0 ⇒ 5d = 3a ⇒ a = .....(1) Given, 6th term exceeds twice 2nd term by 4 a6 = a + 5d a2 = a + d ⇒ a + 5d = 2(a + d) + 4 ⇒ a + 5d = 2a + 2d + 4 ⇒ a + 5d - 2a - 2d = 4 ⇒ 3d - a = 4 ⇒ 3d - a = 4 ...(2) Substituting value of a from equation (1) in equation (2), we get : ⇒ 3d - = 4 ⇒ = 4 ⇒ 4d = 12 ⇒ d = ⇒ d = 3 Substituting value of d in equation (1), we get : ⇒ a = ⇒ a = ⇒ a = 5 By formula, where, a = first term, d = common difference Hence, the sum of the first 9 terms of this A.P. = 153.

Mathematics

18^th term of an A.P. is equal to 4 times its 4^th term and the 6^th term exceeds twice the 2^nd term by 4. Find the sum of the first 9 terms of this A.P.

AP

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If S_n denotes the sum of first n terms of an A.P., prove that :
S₁₂ = 3(S₈ − S₄)

If A, B and C are three arithmetic progressions (APs) as given below :
A = 2, 4, 6, 8, …….. upto n terms
B = 3, 6, 9, 12, …… upto n terms
C = 0, 4, 8, 12, …… upto n terms, then
out of A + B, A - C, C - B and B - A which is/are A.P. ?
A + B
A - C
C - B
All are A.P.

In an A.P. a = -36, d = 18 and l = 36, then n is :
10
5
15
20

Mathematics

18th term of an A.P. is equal to 4 times its 4th term and the 6th term exceeds twice the 2nd term by 4. Find the sum of the first 9 terms of this A.P.

AP

Related Questions

A man saved ₹ 7,65,000 in 10 years. In each year, after the first, he saved ₹ 6,000 more than he did in the preceding year. How much did he save in the first seven years?

If Sn denotes the sum of first n terms of an A.P., prove that :S12 = 3(S8 − S4)

If A, B and C are three arithmetic progressions (APs) as given below :A = 2, 4, 6, 8, …….. upto n termsB = 3, 6, 9, 12, …… upto n termsC = 0, 4, 8, 12, …… upto n terms, thenout of A + B, A - C, C - B and B - A which is/are A.P. ?A + BA - CC - BAll are A.P.

In an A.P. a = -36, d = 18 and l = 36, then n is :1051520

18^th term of an A.P. is equal to 4 times its 4^th term and the 6^th term exceeds twice the 2^nd term by 4. Find the sum of the first 9 terms of this A.P.

If S_n denotes the sum of first n terms of an A.P., prove that :
S₁₂ = 3(S₈ − S₄)

If A, B and C are three arithmetic progressions (APs) as given below :
A = 2, 4, 6, 8, …….. upto n terms
B = 3, 6, 9, 12, …… upto n terms
C = 0, 4, 8, 12, …… upto n terms, then
out of A + B, A - C, C - B and B - A which is/are A.P. ?
A + B
A - C
C - B
All are A.P.

In an A.P. a = -36, d = 18 and l = 36, then n is :
10
5
15
20