a = 7, so
(7+d)/7 = (7+4d)/(7+d)
Now just find d.
Be sure to check the geometric sequence that results.
the first, second and fifth term of a linear sequence is/are three consecutive termsof an exponential sequence, if the first term of linear sequence is 7.find its common difference.
2 answers
In the AS,
7, 7+d, 7+4d form a GS
so
(7+d)/7 = (7+4d)/(7+d)
(7+d)^2 = 7(7+4d)
49 + 14d + d^2 = 49 + 28d
d^2 - 14d = 0
d(d-14) = 0
d = 0 , then all terms would be the same
or
d = 14
if d = 14, then the 1st, 2nd and 5th terms of the AS are : 7, 21 and 63
are 7,21,63 a GS ???
21/7 = 3
63/21 = 3 , YES
The common difference is 14
7, 7+d, 7+4d form a GS
so
(7+d)/7 = (7+4d)/(7+d)
(7+d)^2 = 7(7+4d)
49 + 14d + d^2 = 49 + 28d
d^2 - 14d = 0
d(d-14) = 0
d = 0 , then all terms would be the same
or
d = 14
if d = 14, then the 1st, 2nd and 5th terms of the AS are : 7, 21 and 63
are 7,21,63 a GS ???
21/7 = 3
63/21 = 3 , YES
The common difference is 14
4 answers