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

(i) The given numbers form an A.P. with a = 34 and d = 32 - 34 = -2. Let nth term be 10, as, a n = a + (n - 1)d ∴ 10 = 34 + (n - 1)(-2) ⇒ 10 = 34 - 2n + 2 ⇒ 10 = 36 - 2n ⇒ 2n = 36 - 10 ⇒ 2n = 26 ⇒ n = 13. Hence, the sum of the series 34 + 32 + 30 + .... + 10 is 286. (ii) The given numbers form an A.P. with a = -5 and d = -8 - (-5) = -3. Let nth term be -230, then as, a n = a + (n - 1)d ∴ -230 = -5 + (n - 1)(-3) ⇒ -230 = -5 -3n + 3 ⇒ -230 = -2 - 3n ⇒ -230 + 2 = -3n ⇒ -228 = -3n ⇒ 3n = 228 ⇒ n = 76. Hence, the sum of the series -5 + (-8) + (-11) + .... + (-230) is -8930.

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.

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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.

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

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Mathematics

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

AP GP

Related Questions

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.

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.

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

Mathematics

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

AP GP

Related Questions

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.

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.

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

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

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.