Final answer:
The nth term of the arithmetic sequence is found by determining the common difference and using the nth term formula. The common difference is 0.1, and the nth term formula gives the nth term as 0.1n + 0.9.
Step-by-step explanation:
The question asks for the nᵗʰ term of an arithmetic sequence given that the third term is 1.2 and the fifth term is 1.4. In an arithmetic sequence, the difference between any two consecutive terms, known as the common difference, is constant. To find the common difference, we can subtract the third term from the fifth term, and since there is one term between them, we divide by 2:
Common difference (d) = (1.4 - 1.2) / (5 - 3) = 0.2 / 2 = 0.1
Now that we have the common difference, we can use the formula for the nᵗʰ term of an arithmetic sequence, which is:
an = a1 + (n - 1)*d
Since we know the third term (a3) is 1.2, we can find the first term (a1) by subtracting two times the common difference:
a1 = a3 - 2*d = 1.2 - 2*(0.1) = 1
So the first term is 1. Using the formula we can determine the nᵗʰ term:
an = 1 + (n - 1)*0.1
Finally, we can simplify:
an = 1 + 0.1n - 0.1
an = 0.1n + 0.9
Therefore, the nᵗʰ term of the sequence is 0.1n + 0.9.