Write the mathematical expression that describes the arithmetic sequence.
Use sigma notation to describe the sum of the first ten terms of the arithmetic sequence
20, 18.5, 17, 15.5, 14, (the difference is from -1.5)
Help, please!
term(n) = -1.5n +c
so when n = 1 your want term(1) to be 20
-1.5(1)n + c = 20
c = 21.5
term(n) = -1.5n + 21.5 , where n is a natural number
now just put that in the notation that you must have studied.
To write the mathematical expression that describes the arithmetic sequence, we can use the general formula for an arithmetic sequence:
a_n = a_1 + (n - 1)d
Where a_n represents the nth term of the sequence, a_1 is the first term, n is the position of the desired term, and d is the common difference between terms.
In this case, the first term (a_1) is 20, and the common difference (d) is -1.5.
So, the mathematical expression that describes the arithmetic sequence is:
a_n = 20 + (n - 1)(-1.5)
To find the sum of the first ten terms of the arithmetic sequence using sigma notation, we can use the formula:
S_n = (n/2)(a_1 + a_n)
Where S_n represents the sum of the first n terms of the sequence.
In this case, we need to find the sum of the first ten terms (n = 10) of the arithmetic sequence.
So, the sigma notation to describe the sum of the first ten terms of the arithmetic sequence is:
S_10 = (10/2)(a_1 + a_10)