In an A.P. (with usual notations):
(i) given a = 5, d = 3, a_n = 50, find n and S_n
(ii) given a = 7, a₁₃ = 35, find d and S₁₃
(iii) given d = 5, S₉ = 75, find a and a₉
(iv) given a = 8, a_n = 62, S_n = 210, find n and d
(v) given a = 3, n = 8, S = 192, find d.

Question

In an A.P. (with usual notations):
(i) given a = 5, d = 3, a_n = 50, find n and S_n
(ii) given a = 7, a₁₃ = 35, find d and S₁₃
(iii) given d = 5, S₉ = 75, find a and a₉
(iv) given a = 8, a_n = 62, S_n = 210, find n and d
(v) given a = 3, n = 8, S = 192, find d.

KnowledgeBoat · Accepted Answer

(i) a = 5, d = 3, a_n = 50. By formula a_n = a + (n - 1)d ⇒ 50 = 5 + (n - 1)3 ⇒ 50 = 5 + 3n - 3 ⇒ 50 = 2 + 3n ⇒ 50 - 2 = 3n ⇒ 48 = 3n ⇒ n = 16. By formula Hence, n = 16 and S_n = S₁₆ = 440. (ii) a = 7, a₁₃ = 35 By formula a_n = a + (n - 1)d ⇒ 35 = 7 + (13 - 1)d ⇒ 35 = 7 + 12d ⇒ 35 - 7 = 12d ⇒ 28 = 12d ⇒ d = (Dividing by 4) ⇒ d = By formula S_n = Hence, d = and S_n = S₁₃ = 273. (iii) d = 5, S₉ = 75 By formula S_n = By formula a_n = a + (n - 1)d, Hence, a = (iv) a = 8, a_n = 62, S_n = 210. By formula a_n = a + (n - 1)d ⇒ 62 = 8 + (n - 1)d ⇒ 62 - 8 = (n - 1)d ⇒ (n - 1)d = 54 (Eq 1) By formula S_n = Putting value of (n - 1)d from Eq 1 in above equation, Hence, the value of n = 6 and d = (v) a = 3, n = 8, S = 192. By formula S_n = ⇒ 192 = ⇒ 192 = 4[6 + 7d] ⇒ = 6 + 7d ⇒ 48 = 6 + 7d ⇒ 7d = 42 ⇒ d = 6. Hence, the value of d is 6.

Mathematics

In an A.P. (with usual notations):
(i) given a = 5, d = 3, a_n = 50, find n and S_n
(ii) given a = 7, a₁₃ = 35, find d and S₁₃
(iii) given d = 5, S₉ = 75, find a and a₉
(iv) given a = 8, a_n = 62, S_n = 210, find n and d
(v) given a = 3, n = 8, S = 192, find d.

AP GP

Related Questions

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Find the sums given below:
(i) 34 + 32 + 30 + …. + 10
(ii) -5 + (-8) + (-11) + …. + (-230)

The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.

Mathematics

In an A.P. (with usual notations):(i) given a = 5, d = 3, an = 50, find n and Sn(ii) given a = 7, a13 = 35, find d and S13(iii) given d = 5, S9 = 75, find a and a9(iv) given a = 8, an = 62, Sn = 210, find n and d(v) given a = 3, n = 8, S = 192, find d.

AP GP

Related Questions

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Find the sums given below:(i) 34 + 32 + 30 + …. + 10(ii) -5 + (-8) + (-11) + …. + (-230)

The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.

In an A.P. (with usual notations):
(i) given a = 5, d = 3, a_n = 50, find n and S_n
(ii) given a = 7, a₁₃ = 35, find d and S₁₃
(iii) given d = 5, S₉ = 75, find a and a₉
(iv) given a = 8, a_n = 62, S_n = 210, find n and d
(v) given a = 3, n = 8, S = 192, find d.

Find the sums given below:
(i) 34 + 32 + 30 + …. + 10
(ii) -5 + (-8) + (-11) + …. + (-230)