What is the 28th term of the sequence an = an−1 + 5.2, if the 26th term is 42.3?
Since $a_{26}=42.3$, we know that $a_{27}=a_{26}+5.2=42.3+5.2=47.5.$ Then $a_{28}=a_{27}+5.2=47.5+5.2=\boxed{52.7}.$
To find the 28th term of the sequence, we can use the given information.
Given: aₙ = aₙ₋₁ + 5.2
We know that the 26th term, a₂₆, is 42.3. Let's use this information to find the value of a₂₇.
a₂₆ = a₂₅ + 5.2
42.3 = a₂₅ + 5.2
Now, let's solve for a₂₅:
a₂₅ = 42.3 - 5.2
a₂₅ = 37.1
Now that we know the value of a₂₅, we can find the value of a₂₆:
a₂₆ = a₂₅ + 5.2
a₂₆ = 37.1 + 5.2
a₂₆ = 42.3
Therefore, the 28th term, a₂₈, would be:
a₂₇ = a₂₆ + 5.2
a₂₇ = 42.3 + 5.2
a₂₇ = 47.5
To find the 28th term of the sequence, we need to determine the value of a28.
Given that a26 is 42.3, we can use this information to find a27 and then a28.
The given sequence is defined by the rule: an = an−1 + 5.2.
To find a27, we can use the given value of a26:
a27 = a26 + 5.2
Substituting the value of a26 = 42.3 into the equation:
a27 = 42.3 + 5.2
a27 = 47.5
Now that we have found a27, we can find a28 using the same rule:
a28 = a27 + 5.2
Substituting the value of a27 = 47.5 into the equation:
a28 = 47.5 + 5.2
a28 = 52.7
Therefore, the 28th term of the sequence is 52.7.