The diagram shows the first four patterns of a sequence. Find an expression for the numbers of squares in the nth pattern of the sequence.

n^2+3

Step-by-step explanation:

As we can see in the diagram

1st pattern consists from 1 square 1x1 +3 squares 1x1 each

2nd pattern consists from 1 square 2x2 +3 squares 1x1 each

3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each

4-th pattern consists from 1 square 4x4 + 3 squares 1x1  each

We can to continue :

5-th pattern consists from 1 square 5x5+3 squares 1x1 each

So the nth    pattern consists from 1 square nxn+3 squares 1x1 each

Or total amount of 1x1 squares in nth pattern N= n^2+3

n² + 3

Step-by-step explanation:

The first pattern has 4 squares.

The second pattern has 7 squares.

The third pattern has 12 squares.

The fourth pattern has 19 squares.

When we subtract 3 on each term we get:

1, 4, 9, and 16, which are perfect squares.

So n² is in the formula. Each term is added 3 to the perfect squares.

The nth term becomes n² + 3.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this