CBSE Class 10 Answered
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 | 22 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 | 22 Dec, 2013, 01:00: PM
Application Videos
-
Arithmetic Progression - 1
This video explains the concept of Arithmetic Progression, Solving Linear E... -
Sum of an n Terms of an A.P.
This video explains the concept of how to find the nth term of a Arithmetic... -
nth term of an A.P.
This video explains the concept of nth term of an Arithmetic Progression. -
Arithmetic Progression - 2
This video explains the concept of how to find an Arithmetic Progression. -
Nth term of an AP - 1
This video explains a case study based question covering the concept of ...
Concept Videos
-
Introduction to Arithmetic Progression
This video explains the identification of series which is mathematically kn... -
nth Term of an A.P.
Problems related to the calculation of nth term in an Arithmetic progressi... -
Determine terms of an arithmetic progression
Determine the terms of an arithmetic progression when given the number of t... -
Word Problems of A.P.
This video explains the concept of the nth term and the sum of the first n ... -
Introduction to Arithmetic Progression
This video explains the identification of series, mathematically known as A...
CBSE 10 - Maths
Asked by purbashadebnath1980 | 09 Mar, 2024, 12:10: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by deepikaselvam2009 | 20 Feb, 2024, 08:57: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by keshavsinghalhapur | 16 Jan, 2024, 08:46: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by keshavsinghalhapur | 15 Jan, 2024, 10:56: AM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by durgauikey7000 | 08 Dec, 2023, 08:16: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by skandachiranjeevin | 06 Dec, 2023, 07:08: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by shaikhyakub9946 | 30 Nov, 2023, 11:50: AM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by prassanna.j | 13 Nov, 2023, 11:24: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by prassanna.j | 13 Nov, 2023, 11:23: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by latayadav23 | 17 Oct, 2023, 08:39: PM
ANSWERED BY EXPERT
