Question

QUESTION 2

Answer 1

Answer:

✓2=1.41421

✓5=2.23607

✓8=2.82842

✓11=3.31662

✓14=3.74166

Step-by-step explanation:

Therefore the numbers are increasing by three so they cant be perfect square

Answer 2

9514 1404 393

Answer:

  squares are of the form 3n or 3n+1; the sequence is of the form 3n-1, so none of the sequence will be a square

Step-by-step explanation:

The given arithmetic sequence has first term 2 and common difference 3, so its explicit formula is ...

  an = 2 +3(n -1) = 3n -1 . . . . for counting numbers n

__

All integers are of one of these forms: 3n-1, 3n, 3n+1, for some integer n. The squares of these are ...

  (3n -1)² = 9n² -6n +1 = 3(3n² -2) +1 = 3k+1 for some k

  (3n)² = 3(3n²) = 3k for some k

  (3n +1)² = 9n² +6n +1 = 3(3n² +2) +1 = 3k+1 for some k

Note that none of these squares is of the form 3n -1.

Hence, the square of an integer cannot be in the given sequence.