the first term of an arithmetic sequence is 8, the last term id 56 and the sum is 416. find the number of terms

13

Step-by-step explanation:

first term (a) = 8

last term ( ) = 56

sum (S) = 416

number of terms (n) = ?

                              equation

                              S = n/2 (a+)

                             416 = n/2 (8+56)

                             416 = n/2 (64)

                              416 = 32n

                               n = 416/32 = 13

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.