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in Arithmetic Progression by (56.3k points)

The first and the last terms of an A.P are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

1 Answer

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Best answer

Given,

First term (a) = 5 and the last term (l) = 45

Also, Sn = 400

We know that,

an = a + (n – 1)d

⟹ 45 = 5 + (n – 1)d

⟹ 40 = nd – d

⟹ nd – d = 40  ….. (1)

Next,

Sn = \(\frac{n}{2}\)(2(5) + (n − 1)d)

⟹ 400 = n[10 + nd – d]

⟹ 800 = n[10 + 40] [using (1)]

⟹ 800 = 50n

⟹ n = 16 …. (2)

So, by substituting (2) in (1), we have

nd – d = 40

⟹ 16d – d = 40

⟹ 15d = 40

⟹ d = \(\frac{8}{3}\)

Therefore, the common difference of the given A.P. is \(\frac{8}{3}\).

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