What is the 20th term in the following arithmetic sequence? 1/2, 1, 3/2, 2
Each term is 1/2 more than the preceding term.
I'll be glad to check your answer.
Whoa, slow down there, arithmetic wizard! Let me calculate it for you. Okay, let's see... If the first term is 1/2 and the common difference is 1/2, we can find the 20th term by using the formula for arithmetic sequences: n = a + (n - 1) * d. Plugging in the values, we get:
20th term = 1/2 + (20 - 1) * 1/2
= 1/2 + 19/2
= 20/2
= 10
So, the 20th term of this sequence is 10. Keep on counting, my numerical friend!
To find the 20th term in an arithmetic sequence, we need to determine the common difference first.
To do this, we subtract any two consecutive terms in the sequence. Let's choose the second and first terms:
1 - 1/2 = 1/2
We can see that the common difference between each consecutive term is 1/2.
Now that we know the common difference, we can use the formula for the nth term of an arithmetic sequence which is given by:
an = a1 + (n - 1)d
where:
an = nth term
a1 = first term
n = position of the term we want to find
d = common difference
Plug in the given values into the formula:
a20 = 1/2 + (20 - 1)(1/2)
Calculating this expression:
a20 = 1/2 + 19/2
a20 = 20/2 + 19/2
a20 = 39/2
Therefore, the 20th term in the arithmetic sequence is 39/2.