Identify the 42nd term of an arithmetic sequence where a_1=-12 and a_27=66

a₄₂ = 107

Step-by-step explanation:

The nth term of an arithmetic sequence is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₂₇ = 66 , then

a₁ + 26d = 66 , that is

- 12 + 26d = 66 ( add 12 to both sides )

26d = 78 ( divide both sides by 26 )

d = 3

Then

a₄₂ = - 16 + (41 × 3) = - 12 + 123 = 111

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.