Please help. I don't understand this question. Can you explain? https://s1.postimg.org/6d4j0atp6n/1234567.png?

2.
a.
The common difference:
T(2) - T(1) = T(3) - T(2)
(5k + 2) - (k + 4) = (10k - 2) - (5k + 2)
5k + 2 - k - 4 = 10k - 2 - 5k - 2)
4k - 2 = 5k - 4
k = 2


b.
T(1) = 2 + 4 = 6
T(2) = 5(2) + 2 = 12
T(3) = 10(2) - 2 = 18


c.
T(2) - T(1) = 12 - 6 = 6
T(3) - T(2) = 18 - 12 = 6
The common difference = 6


d.
The first term, a = T(1) = 6
The common difference, d = 6

The 25th term, T(25)
= a + (n - 1)d
= 6 + (25 - 1) * 6
= 150


e.
Sum of the first 25 terms, S(25)
= n [2a + (n - 1)d] / 2
= 25 [2 * 6 + (25 - 1) * 6] / 2
= 1950

　
Question:

The first three terms of an arithmetic sequence are:
k+4, 5k+2, 10k−2

a. Show that k = 2.
b. Find the values of the first three terms of the sequence.
c. Write down the value of the common difference.
d. Calculate the 25th term of the sequence.
e. Find the sum of the first 25 terms of the sequence.

Answer:

a.

When x, y, z are in arithmetic sequence, then difference between successive terms are the same:
y−x = z−y

Since k+4, 5k+2, 10k−2 are in arithmetic sequence, then:
(5k+2)−(k+4) = (10k−2)−(5k+2)
4k − 2 = 5k − 4
−k = −2
k = 2

b.

k+4 = 2+4 = 6
5k+2 = 10+2 = 12
10k−2 = 20−2 = 18

c.

Common difference:d = 12−6 = 6

d.

n-th term = 6+6(n−1) = 6n
25th term = 6*25 = 150

e.

Sum of first n terms = n * (a1 + an) / 2

Sum of first 25 terms = 25*(6+150)/2 = 1950