SOLUTION: please i need help with these questions. 1. given that(2-3k),(2k+3),(k+7), where k is a constant, are three consecutive terms of linear sequence(A.P),find its common difference.

Question 1067633: please i need help with these questions.
1. given that(2-3k),(2k+3),(k+7), where k is a constant, are three consecutive terms of linear sequence(A.P),find its common difference.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The nth term of a arithmetic sequence is
:
a(n) = a(1) + d(n-1), where a(1) is the first term and d is the common difference
:
we are given
:
2-3k = a(1) + d(n-1)
3+2k = a(1) + d(n+1-1) = a(1) + dn
7+k = a(1) + d(n+2-1) = a(1) + d(n+1)
:
by the definition of an arithmetic sequence, we know that
:
3+2k - (2-3k) = 7+k - (3+2k)
:
5k + 1 = -k + 4
:
6k = 3
;
k = 3/6 = 1/2
:
***************************
d = 5(1/2) + 1 = 7/2 = 3.5
***************************
:

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