The sum of the first terms of an Arithmetic progression (Ap) is 130.if the fifth term is 3times, the first term, find the (a)common difference (b)first term (c)number of terms of the Ap if the last term is 28.

For part a)

130 = 10/2[2a+(10-1)d]

Simplify, u get

2a + 9d = 26(1)

Also U5 = a + (5-1)d = 3a

Simplify, u get

a= 2d(2)

Substituting for a in equation 1,

2(2d)+9d= 26

Solving for d, we get

d = 2

In part b) substituting for d in equation 2 to get the first term

a = 2(2) = 4

Part c) the no. of terms required can be obtained by solving

28 = 4+(n-1)2

n = 13

if you need just tell me and i will come to the rescue.

step-by-step explanation:

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.