Show that a 1 , a 2 , a 3 , ..... form an A.P. where a n is defined as a n = 3 + 4n. Also find the sum of first 15 terms.

a n = 3 + 4n a 1 = 3 + 4 × 1 = 3 + 4 = 7 a 2 = 3 + 4 × 2 = 3 + 8 = 11 a 3 = 3 + 4 × 3 = 3 + 12 = 15 a 4 = 3 + 4 × 4 = 3 + 16 = 19. Since, a 4 - a 3 = a 3 - a 2 = a 2 - a 1 = 4, i.e any term - preceding term = fixed number = 4. ∴ a 1 , a 2 , a 3 ..... form an A.P. By formula S n = Hence, the sum of first 15 terms of the A.P. is 525.

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.

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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.

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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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In an A.P., the sum of its first n terms is 6n - n². Find its 25th term.

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Mathematics

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.

AP GP

Related Questions

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.

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.

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.

In an A.P., the sum of its first n terms is 6n - n². Find its 25th term.

Mathematics

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.

AP GP

Related Questions

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.

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.

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.

In an A.P., the sum of its first n terms is 6n - n2. Find its 25th term.

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.

In an A.P., the sum of its first n terms is 6n - n². Find its 25th term.