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

Let first term of A.P. be a and common difference be d. By formula, a n = a + (n - 1)d Given, 2nd term = 14 ⇒ a 2 = 14 ⇒ a + (2 - 1)d = 14 ⇒ a + d = 14 ............(1) 3rd term = 18 ⇒ a 3 = 18 ⇒ a + (3 - 1)d = 18 ⇒ a + 2d = 18 ............(2) Subtracting equation (1) from (2), we get : ⇒ a + 2d - (a + d) = 18 - 14 ⇒ a - a + 2d - d = 4 ⇒ d = 4. Substituting value of d in equation (1), we get : ⇒ a + 4 = 14 ⇒ a = 10. Last term (l) = 51st term = a 51 = a + (51 - 1)d = 10 + 50 × 4 = 10 + 200 = 210. By formula, Sum (S) = Substituting values we get : Hence, sum of first 51 terms = 5610.

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

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

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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.

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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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Mathematics

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

AP

Related Questions

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

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

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.

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.

Mathematics

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

AP

Related Questions

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

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

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.

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.

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.