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Algebra

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 Joined: 16 Sep 2011 Post: 23
15 Oct 2011 20:42:04 IST
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Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

In an AP a1,a2,a3,a4..........a24   terms are there if   a1+a5+a10+a15+a19+a24=225 then wat is sum of a1+a2+a3+.......+a24

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
17 Oct 2011 12:47:30 IST
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a1 + a24 = a10 + a15

in an AP the sum of the terms equidistant from both the ends is equal to the sum of the first and last term.

the question should have been -

a1+a5+a10+a15+a20+a24=225

New kid on the Block

Joined: 16 Sep 2011
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17 Oct 2011 18:23:10 IST
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so wat is sum of 24 terms plz answer

Blazing goIITian

Joined: 27 Dec 2010
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19 Oct 2011 12:14:36 IST
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a1+a5+a10+a15+a20+a24=225

if this is what the question says then -

a1 + a24 = a10 + a15 = a20 + a5

so we get 3(a1 + a24) = 225

or, a1 + a24 = 75

so the sum is simply (24/2)(75) = 900

New kid on the Block

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21 Oct 2011 03:24:35 IST
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awesome dude

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Joined: 1 Dec 2006
Posts: 2108
20 Feb 2012 11:04:17 IST
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a1+a5+a10+a15+a20+a24=225

=> a + (a+4d) + (a+9d) + (a+10d) + (a+19d) + (a+23d) = 225
=> 6a +  69 d = 225=> 2a + 23 d = 75

sum of 24 terms = 2a+ 23d = 75

Hot goIITian

Joined: 13 Nov 2011
Posts: 157
20 Feb 2012 22:06:59 IST
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sum of six terms in AP between fixed extremities =225

So sum of 6x4=24 terms in Ap between same fixed extrimities =4x225=900.

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