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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’.

Here, a_n = 4, d = 2
S_n = –14
We know that,

a_n = a + (n -1)d
$rightwards double arrow$ 4 = a + (n -1) x 2
$rightwards double arrow$ 4 = a + 2n - 2
$rightwards double arrow$ a + 2n = 6 $rightwards double arrow$ a = 6 - 2 n ....(i)

And. Sn = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ [2a+ (n - 1)d]
$rightwards double arrow$ - 14 = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
$rightwards double arrow$ - 28 = n[2a + 2 (n -1) ]
$rightwards double arrow$ - 28 = 2n [a + (n -1)]
$rightwards double arrow$ - 14 = n[a + (n - 1)] ......(ii)

Putting the value of (i) in (ii), we get,
– 14 = n [6 – 2n + n – 1]
⇒ – 14 = n[5 – n]
⇒ –14 = 5n – n²⇒ n² –5n – 14 = 0
⇒ (n – 7) (n + 2) = 0
⇒ n – 7 = 0 or n + 2 = 0
⇒ n = 7 or n = –2
But n cannot be –ve. ∴ n = 7.
Putting this value of V in equation (i), we get
a + 2 x 7 = 6
⇒ a = 6 – 14 = – 8
Hence, n = 7 and a = –8

752 Views

236.

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

631 Views

237.

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

477 Views

Long Answer Type

238.

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

174 Views

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.

101 Views

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 ?

103 Views