Answer:
(3ab)/(2(b-a))
Step-by-step explanation:
The n-th term of an arithmetic progression is ...
an = a1 +d(n -1)
Then the value of n is ...
n = (an -a1)/d +1
The sum of an arithmetic progression is the product of the number of terms and the average of the first and last terms. In this sequence, the common difference d is ...
d = (b -a)
So, the sum is ...
Sn = (a +2a)/2·((2a -a)/(b -a) +1)
Sn = (3ab)/(2(b-a)) . . . . sum of the arithmetic progression
__
<u>Example</u>:
The sequence 1, 1.5, 2 has ...
a = 1, b = 1.5
Its sum is given by the above formula as ...
Sn = 3(1)(1.5)/(2(1.5 -1)) = 4.5/(2(.5)) = 4.5 = 1 + 1.5 + 2 . . . . yes
