Answer:
d = 7
Step-by-step explanation:
The first five terms of an arithmetic progression are
a, a + d, a + 2d, a + 3d, a + 4d
Where d is the common difference
Given the fifth term term = 41, then
a + 4d = 41 → (1)
Given the sum of the first four terms = 94, then
a + a + d + a + 2d + a + 3d = 94, that is
4a + 6d = 94 → (2)
Rearrange (1) expressing a in terms of d by subtracting 4d from both sides
a = 41 - 4d → (3)
Substitute a = 41 - 4d into (2)
4(41 - 4d) + 6d = 94 ← distribute and simplify left side
164 - 16d + 6d = 94
164 - 10d = 94 ( subtract 164 from both sides )
- 10d = - 70 ( divide both sides by - 10 )
d = 7 ← common difference
