a1,a2,a3,...a24 are in AP and a1+a5+a10+a15+a20+a24=300.find the sum of first 24 terms of the AP

Asked by science field | 22nd Dec, 2013, 12:47: PM

Expert Answer:

We need to find :
 
a1+a2+a3+........a24.
 
Given : a1+a5+a15+a20+a24 = 300.
 
If a given series is in AP, a subset of the series is also in AP.
 
Let a1,a2,a3....a24 be an AP with common difference d.
 
Thus, a5, a10,a15,a20 will also be an AP, but with common difference 5d.
 
Thus, the sum a1+a2+a3+....a24 = 24(a1+a24)/2 = 12(a1 +a24)
 
Also, the sum a5+a10+a15+a20 = 4(a5 + a20)/2 = 2(a1+4d+a24-4d)
                                                                       = 2(a1+a24)
 
Thus, 2(a1+a24) + a1+a24 = 300
Thus, 3(a1+a24) =300
Thus, a1+a24=100
 
Thus, a1+a2+a3.......a24 = 12(100) = 1200

Answered by Vimala Ramamurthy | 22nd Dec, 2013, 01:00: PM

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