What is the 28th term of the sequence an = an−1 + 5.2, if the 26th term is 42.3?
To find the 28th term of the sequence, we can use the given information that the 26th term is 42.3 and the recursive formula an = an−1 + 5.2.
We can start by finding the 27th term of the sequence:
a27 = a26 + 5.2
a27 = 42.3 + 5.2
a27 = 47.5
Now, to find the 28th term, we can use the same formula:
a28 = a27 + 5.2
a28 = 47.5 + 5.2
a28 = 52.7
Therefore, the 28th term of the sequence is 52.7.
To find the 28th term of the sequence, we can use the given information that the 26th term is 42.3.
Let's write out the first few terms of the sequence to see if we can identify a pattern:
a1 = a0 + 5.2
a2 = a1 + 5.2 = (a0 + 5.2) + 5.2 = a0 + 2 * 5.2
a3 = a2 + 5.2 = (a0 + 2 * 5.2) + 5.2 = a0 + 3 * 5.2
a4 = a3 + 5.2 = (a0 + 3 * 5.2) + 5.2 = a0 + 4 * 5.2
...
From this pattern, we can see that each term is equal to the initial term (a0) plus a multiplication of (n - 1) and 5.2.
So, for the 26th term, which is a2, we have:
a2 = a0 + 2 * 5.2 = 42.3
Now, let's rearrange this equation to solve for a0:
a0 = 42.3 - 2 * 5.2 = 42.3 - 10.4 = 31.9
Finally, let's use this information to find the 28th term, which is a4:
a4 = a0 + 4 * 5.2 = 31.9 + 4 * 5.2 = 31.9 + 20.8 = 52.7
Therefore, the 28th term of the sequence is 52.7.