This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have been given that the sums of first n terms of three A.P.s are S1, S2 and S3.
Also the first term of each is 5 and their common differences are 2, 4 and 6 respectively.
Now we have to prove that S1 + S3 = 2S2
CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 59
By using the formula of the sum of n terms of an A.P.
Sn = n[2a +(n – 1)d] / 2
According to the question,
S1 = n[2(5)+(n – 1)2] / 2 = n[8 + 2n] / 2 = 4n + n2
S2 = n[2(5) + (n – 1)4] / 2 = n[6 + 4n] / 2 = 3n + 2n2
S3 = n[2(5) + (n – 1)6] / 2 = n[4 + 6n] / 2 = 2n + 3n2
Now, L.H.S. = (4n + n2) + (2n + 3n2)
= 6n + 4n2
= 2[3n + 2n2]
= 2S2
Hence proved.