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Arithmetic Progressions

Short Answer Type

231. The 17th term of an A .P. exceeds the 10th term by 7. Find the common difference.

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232. Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 100th terms?

Let the common difference of both the
A.P.’s = d
and First term of Ist A.P. = a
also first term of 2nd A .P. = b
Then, 200th term of 1st A .P. = a + 99d
and 100th term of IInd A .P. = b + 99d
Difference between their 100th term = 100
(given)
⇒ (a + 99d) – (b + 99d) = 100
⇒ a – b = 100 ...(i)
Now, a₁₀₀₀ of Ist A.P. = a + 999d
and a₁₀₀₀ of Ilnd A .P. = b + 999d
Hence, difference between their 1000th terms
= (a + 999d) (b + 999d) = a – b
= 100. [Using (i)]

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233.

In an A.P. :
Given a = 2, d = 8, S_n = 90, find ‘n’ and a_n

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234.

In an A.P.
Given a = 8, a_n = 62, S_n = 210, find ‘n’ and ‘d’.

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235.

In an A.P.
Given a_n = 4, d = 2, S_n = –14, find ‘n’ and ‘a’.

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236.

In an A.P.
Given a = 3, n = 8, S = 192, find ‘d’.

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237.

In an A.P.
Given l = 28, S = 144, n = 9, find ‘a’.

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Long Answer Type

238.

How many terms of the A.P. 9, 17, 25, ... must be taken to give a sum of 636?

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Short Answer Type

239.

The first term of an AP 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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240. The first and the last term 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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