The first equation is: #" "n + n + x = 15 #
The second equation is: #" " n + 2x + n + 3x = 43. #
#n# is the first term #x# is the variable of the sequence. so
#n + x" "# is the second term
#n + 2x" "# is the third term
#n + 3x" "# is the fourth term.
Solving for x in terms of
# n + 2x + n + 3x = 43 " "# adding like terms.
# 2n + 5x = 43" " # subtracting #5x# from both side sides gives
# 2n + 5x -5x = 43 -5x" " # resulting in
# 2n = 43 -5x" " # this can be substituted into the first equation.
# n + n + x = 15" "# which is the same as
# 2n + x = 15" " # now substitute # 2n = 43 -5x# into the question.
# 43 -5x + x = 15" " # combine like terms
# 43 - 4x = 15# add #4x# to both sides and subtract #15# from both sides
# 43 -15 - 4x + 4x = 15-15 + 4x" "# gives.
# 28 = 4x " "# Divide both sides by #4# to solve for #x #
# 28/4 = (4x)/4 # gives
# 7 = x " "# This is the variable of the sequence.
Putting #7# in for #x# to solve for #n# the first number in the sequence.
#n + n + 7 = 15" "# combine like terms
# 2n + 7 = 15" "# subtract 7 from both sides
# 2n + 7 -7 = 15 -7 " "# which gives
# 2n = 8 " "# Divide both sides by 2
# (2n)/2 = 8/2 # gives
#n = 4# so #4# is the first number of sequence add #7#
# n_2 = 11" " 4 + 7 = 11#
#n_3 = 18" " 11 +7 = 18#
#n_4 = 25" "18 + 7 = 25#