Final answer:
To find the next three terms in the sequence a₍=2ⁿ+1/2ⁿ+1, we substitute n=2, n=3, and n=4 into the formula. The sequence produces the value of 1 for each of these terms, showing that it is a constant sequence where every term equals 1.
Step-by-step explanation:
To write the next three terms of the sequence a₍=a₁+1/2ⁿ+1, we need to substitute the values of n into the given sequence formula. For the sequence {a₍}₍=1[infinity], the next three terms after n=1 will correspond to n=2, n=3, and n=4.
For n=2, a₂ would be 2²+1/2²+1, which simplifies to 5/5, or 1.
For n=3, a₃ would be 2³+1/2³+1, which simplifies to 9/9, or 1.
For n=4, a₄ would be 2⁴+1/2⁴+1, which simplifies to 17/17, or 1.
Thus, the next three terms in the sequence are all 1, because the sequence is composed of terms that always equal 1 regardless of the value of n.