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

Question

KnowledgeBoat · Accepted Answer

By formula, where, a = first term, d = common difference Subtracting equation (3) from equation (2), we get : ⇒ S8 - S4 = (8a + 28d) - (4a + 6d) ⇒ S8 - S4 = 8a + 28d - 4a - 6d ⇒ S8 - S4 = 4a + 22d Multiplying the above equation by 3, we get : ⇒ 3(S8 - S4) = 3(4a + 22d) ⇒ 3(S8 - S4) = 12a + 66d ⇒ 3(S8 - S4) = S12 Hence, proved that S12 = 3(S8 − S4).

Mathematics

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

AP

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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 A, B and C are three arithmetic progressions (APs) as given below :
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Mathematics

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

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?

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.

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.

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

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 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.