The 5th term of an AP is -3. The 6th term is equal to the 1st term multiplied by (-1).
Find the first term and the common difference.
Find the sum of the first 25 terms of the AP.
can anyone help me get started on this?
many thanks
Let a= 1st term
Let d= difference common between terms.
The sequence is..
a, (a+d), (a+2d), (a+3d), (a+4d), (a+5d),....
The 5th term (a+4d) is -3
The 6th term (a+5d) is -a
Then the difference between these is (a+5d)-(a+4d)=5d-4d=d=-a-(-3)=3-a
Also, a+5d = -a, so 2a+5d = 0, so 2a = -5d = -5(3-a) = 5a-15.
2a=5a-15
15=5a-2a=3a
Solving for "a" allows "d" to be determined.
The sum of an arithmetic sequence is
The average is
Hence
The first term is "a".