The fifth term of an arithmetic progression is 41 and the sum of the first four terms is 94. find the common difference.

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

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step-by-step explanation:

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