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.

Let nth be the last term so, a = 5, l = a n = 45, S n = 400. By formula a n = a + (n - 1)d ⇒ 45 = 5 + (n - 1)d ⇒ 45 - 5 = (n - 1)d ⇒ (n - 1)d = 40 (Eq 1) By formula S n = Putting value of (n - 1)d from Eq 1 in above equation, Putting value of n in Eq 1 we get, Hence, number of terms = 16 and common difference =

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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The first and the last terms of an A.P. 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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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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Find the sums given below:
(i) 34 + 32 + 30 + …. + 10
(ii) -5 + (-8) + (-11) + …. + (-230)

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Mathematics

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.

AP GP

Related Questions

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

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

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)

Mathematics

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.

AP GP

Related Questions

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

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

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.

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.

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