Mathematics
If A, B and C are three arithmetic progressions (APs) as given below :
A = 2, 4, 6, 8, …….. upto n terms
B = 3, 6, 9, 12, …… upto n terms
C = 0, 4, 8, 12, …… upto n terms, then
out of A + B, A - C, C - B and B - A which is/are A.P. ?
A + B
A - C
C - B
All are A.P.
Answer
Given,
A = 2, 4, 6, 8, …….. upto n terms
B = 3, 6, 9, 12, …… upto n terms
C = 0, 4, 8, 12, …… upto n terms, then
A + B = 2 + 3, 4 + 6, 6 + 9, 8 + 12, ……..
= 5, 10, 15, 20, ……….
The above list is an A.P. with common difference = 5.
A - C = 2 - 0, 4 - 4, 6 - 8, 8 - 12, ……
= 2, 0, -2, -4, ………
The above list is an A.P. with common difference = -2.
C - B = 0 - 3, 4 - 6, 8 - 9, 12 - 12,………
= -3, -2, -1, 0, ………
The above list is an A.P. with common difference = 1.
Hence, Option 4 is the correct option.
Related Questions
If Sn denotes the sum of first n terms of an A.P., prove that :
S12 = 3(S8 − S4)
18th term of an A.P. is equal to 4 times its 4th term and the 6th term exceeds twice the 2nd term by 4. Find the sum of the first 9 terms of this A.P.
In an A.P. a = -36, d = 18 and l = 36, then n is :
10
5
15
20
Do the numbers 12, 52, 72, 73 ….. form an A.P. ? If yes, its next term will be :
Yes, 112
No
Yes, 97
Yes, 24