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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?

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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’.

Here a = 3, n = 8
S = 192
We know that,
$straight S subscript straight n equals straight n over 2 left square bracket 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d right square bracket$
$therefore space space space space 192 space equals space 8 over 2 left square bracket 2 cross times 3 plus left parenthesis 8 minus 1 right parenthesis straight d right square bracket rightwards double arrow space space space space 192 over 4 equals 6 space plus space 7 straight d$
$rightwards double arrow$ 6 +7d = 48
$rightwards double arrow space space space space straight d space equals space 42 over 7 equals 6$
Hence, d = 6 Ans.

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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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