Arithmetic Sequence
The values of a and b is a = 2 and b=3
Explanation:
Given the terms of the arithmetic sequence are
2 , a - b , 2a + b + 7, a - 3b
Let the common difference be D
Therefore,
The difference between the first two consecutive terms is
(a – b) – 2 = D ------------------------------( 1 )
The difference between the next two consecutive terms is
D = (2a + b+7) – ( a - b ) ---------------------(2 )
Equating equation 1 and equation 2
⇒ (a – b) -2 =(2a+b+7)-(a-b)
⇒ a – b – 2 = a + 2b +7
⇒ 3b = -9
⇒ b = -3
Similarly
The difference between the next two consecutive terms is
D = (a-3b)-(2a+b+7) ------- (3)
⇒ (a-3b)-(2a+b+7)=(2a+b+7)-(a-b)
⇒ a-3b)-(2a+b+7) -a - 4b -7 === a+2b+7
⇒ 2a = - ( 14 + 6b)
⇒ a = -( 7 + 3b)
⇒ a = - ( 7 – 3*3 )
Thus the value of a = 2
Hence , the values of a and b is a = 2 and b=3