If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Let first term be a and common difference be d. By formula, S n = Given, Sum of first 7 terms = 49 Given, Sum of first 17 terms = 289 Subtracting equation (1) from (2), we get : ⇒ a + 8d - (a + 3d) = 17 - 7 ⇒ a - a + 8d - 3d = 10 ⇒ 5d = 10 ⇒ d = = 2. Substituting value of d in equation (1), we get : ⇒ a + 3 × 2 = 7 ⇒ a + 6 = 7 ⇒ a = 1. Hence, sum of first n terms = n 2 .

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

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

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Show that a₁, a₂,……., a_n,…….. form an AP where a_n is defined as below :
(i) a_n = 3 + 4n
(ii) a_n = 9 - 5n
Also find the sum of the first 15 terms in each case.

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If the sum of the first n terms of an AP is 4n – n², what is the first term (that is S₁)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

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Mathematics

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

AP

Related Questions

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

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

Show that a₁, a₂,……., a_n,…….. form an AP where a_n is defined as below :
(i) a_n = 3 + 4n
(ii) a_n = 9 - 5n
Also find the sum of the first 15 terms in each case.

If the sum of the first n terms of an AP is 4n – n², what is the first term (that is S₁)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Mathematics

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

AP

Related Questions

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

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

Show that a1, a2,……., an,…….. form an AP where an is defined as below :(i) an = 3 + 4n(ii) an = 9 - 5nAlso find the sum of the first 15 terms in each case.

If the sum of the first n terms of an AP is 4n – n2, what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Show that a₁, a₂,……., a_n,…….. form an AP where a_n is defined as below :
(i) a_n = 3 + 4n
(ii) a_n = 9 - 5n
Also find the sum of the first 15 terms in each case.

If the sum of the first n terms of an AP is 4n – n², what is the first term (that is S₁)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.