Çözüldü Arithmetic Sequence - Undetermined Coefficients Rule - Two-Variable Linear Equation System

If the nth term of a sequence is defined to be 4n + 3, what is the sum of the first term and the difference between the 50th and 45th terms?

Common Difference of The Sequence: r
a1 + [ a1 + (50 - 1)·r ] - [ a1 + (45 - 1)·r ] = a1 + (49 - 44)·r = a1 + 5·r....(I)
a(n) = a1 + (n - 1)·r = 4n + 3 ⇒ a1 + n·r - r = 4n + 3 ⇒ a1 - r = 3....(II) ve n·r = 4n....(III)
From the equations (III) and (II), r = 4....(IV) and a1 = 7....(V)
Using the values (IV) and (V) in (I), 7 + 5·4 = 27.

Original Question:
The nth term of a sequence is defined to be 4n + 3. The 50th term is how much greater than the 45th term?

A) 5
B) 16
C) 20
D) 23
E) 24

https://dynamicpapers.com/wp-content/uploads/2019/12/Test-6.pdf
(Page 15, Section 2, Question 12)