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