If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

Given, S 6 = 36 and S 16 = 256. By formula S n = ⇒ S 6 = ⇒ 36 = 3[2a + 5d] ⇒ 2a + 5d = 12 ⇒ 2a = 12 - 5d (Eq 1) By formula S n = ⇒ S 16 = ⇒ 256 = 8[2a + 15d] ⇒ 2a + 15d = 32 ⇒ 2a = 32 - 15d Putting value of 2a from Eq 1 in above equation, ⇒ 12 - 5d = 32 - 15d ⇒ -5d + 15d = 32 - 12 ⇒ 10d = 20 ⇒ d = 2. ∴ From Eq 1, ⇒ 2a = 12 - 5d ⇒ 2a = 12 - 5(2) ⇒ 2a = 2 ⇒ a = 1. By formula S n = ⇒ S 10 = ⇒ S 10 = 5[2 + 18] ⇒ S 10 = 5 × 20 ⇒ S 10 = 100. Hence, the sum of first 10 terms of the A.P. is 100.

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Mathematics

If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

AP GP

Related Questions

The sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is 1 : 3. Calculate the first and the thirteenth term.

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Show that a₁, a₂, a₃, ….. form an A.P. where a_n is defined as a_n = 3 + 4n. Also find the sum of first 15 terms.

Mathematics

If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

AP GP

Related Questions

The sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is 1 : 3. Calculate the first and the thirteenth term.

Find the sum of first 51 terms of the A.P. whose second and third terms are 14 and 18 respectively.

The 4th term of an A.P. is 22 and 15th term is 66. Find the first term and the common difference. Hence, find the sum of first 8 terms of the A.P.

Show that a1, a2, a3, ….. form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.

Show that a₁, a₂, a₃, ….. form an A.P. where a_n is defined as a_n = 3 + 4n. Also find the sum of first 15 terms.