If the first and third terms equal to 14 and the second and fourth terms equal to 30, what is d?

2 Answers
Sep 1, 2016

Answer:

#d = 8#

Explanation:

Write a systems of equations, with respect to #d# and #t_3#.

#t_3 - d + t_3 + d = 30#

#t_3 + (t_3 - 2d) =14#

However, when we look at the first equation, we realize a system wasn't necessary. The d's cancel out to give the following:

#2t_3 = 30#

#t_3 = 15#

Substituting into the second equation:

#15 + 15 - 2d = 14#

#30 - 2d = 14#

#-2d = -16#

#d = 8#

Hopefully this helps!

Sep 1, 2016

Answer:

#d=8#

Explanation:

Although it is not mentioned, as questioner has mentioned #d#, it is apparent that he is talking about arithmetic sequence with common difference #d#.

Let the numbers be #a, a+d, a+2d, a+3d#. Hence as first and third term add up to #14# and second and fourth term add upto #30#,,

#a+a+2d=14# i.e. #2a+2d=14# and #a+d+a+3d=30# i.e. #2a+4d=30#.

Subtracting first from second equation, we get #2d=16# or #d=8# and putting this in first we get

#2a+16=14# i.e. #2a=-2# and #a=-1#.

Hence series is #{-1,7,15,23}#