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.

The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.

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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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Mathematics

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

AP GP

Related Questions

The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.

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.

Mathematics

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

AP GP

Related Questions

The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.

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.

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.