Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

The first and last terms of an A.P. are a and b. There are altogether (2n + 1) terms. A new series is formed by multiplying each of the first 2n terms by the next term. Find the sum of new series
Asked by rushabhjain.av | 02 Nov, 2019, 10:10: PM
answered-by-expert Expert Answer
First term = a and last term = b
Let d be the common difference of an A.P.
The new series formed is
a(a+d), (a+d)(a+2d), (a+2d)(a+3d), ....., (a+2n)b, b
Sum of this new series 
= a(a+d) + (a+d)(a+2d) + (a+2d)(a+3d) +.....+ (a+2n)b + b
= (a+d)(a+a+2d) + (a+3d)(a+2d+a+4d) + ... + (a+(2n-1)d)(a+(2n-2)d+a+2nd)+b
= 2(a+d)2 + 2(a+3d)2 + .... + 2(a+(2n-1)d)2 + b
= 2[(a+d)2 + (a+3d)2 + .... + (a+(2n-1)d)2]+b
a+d, a+3d, ... a+(2n-1)d forms an A.P. with first term a+d and common difference 2d
Now, use the formula for sum of squares of n terms of an A.P.
, where a+d is the first term, 2d is the common difference and n is the number of terms
Answered by Renu Varma | 07 Nov, 2019, 11:02: AM
CBSE 12-science - Maths
Asked by klmn445 | 03 Apr, 2024, 11:33: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by cherrycharishma512 | 01 Apr, 2024, 12:32: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by shirishakuruva477 | 28 Mar, 2024, 09:52: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by sheensvlog | 27 Mar, 2024, 10:15: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by jprathamesh023 | 23 Mar, 2024, 04:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by antra1799 | 18 Mar, 2024, 07:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by nainaadityathakur | 12 Mar, 2024, 01:22: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by suman0987tewary | 27 Feb, 2024, 03:40: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×