Find the 20th term for 5,-5,-15,-25
Arithemetic, distance is -10, first term 5, n=20
an = a1 + ( n − 1 ) d
To find the 20th term in the sequence 5, -5, -15, -25, we need to determine the pattern or rule that governs the sequence.
By observing the given sequence, we can see that each term is obtained by subtracting 10 from the previous term. Thus, the pattern or rule is to subtract 10 from each term to obtain the next term.
Now we can use this pattern to find the 20th term:
Term 1: 5
Term 2: 5 - 10 = -5
Term 3: -5 - 10 = -15
Term 4: -15 - 10 = -25
We can see that we are subtracting 10 from each term to get the next term. Therefore, to find the 20th term, we subtract 10 from the 19th term.
Term 19: -25 - 10 = -35
Thus, the 20th term in the sequence is -35.
To find the 20th term in a sequence, we need to identify the pattern and then apply it to calculate the desired term.
Given the sequence: 5, -5, -15, -25, ...
We can observe that each term is decreasing by 10. Therefore, the nth term of this sequence can be expressed as:
a(n) = a(1) + (n-1)d
where a(n) is the nth term, a(1) is the first term, n is the term number, and d is the common difference.
In this case, a(1) = 5 and d = -10, as the terms are decreasing by 10.
Now we can substitute the values into the formula to find the 20th term:
a(20) = 5 + (20-1) * (-10)
= 5 + 19 * (-10)
= 5 - 190
= -185
Therefore, the 20th term in the sequence 5, -5, -15, -25 is -185.