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
We need to find :
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)
Thus, 2(a1+a24) + a1+a24 = 300
Thus, 3(a1+a24) =300
Thus, a1+a2+a3.......a24 = 12(100) = 1200
Answered by Vimala Ramamurthy | 22nd Dec, 2013, 01:00: PM
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Verify mobile number
Enter the OTP sent to your number