79.9k views
4 votes
The 4th term of an A.P. is 27. and the sum of the 1st and the fourth term is 42. Find the common difference

1 Answer

5 votes

Answer:

d = 4

Explanation:

the nth term of an AP is


a_(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₄ = 27 , then

a₁ + 3d = 27 → (1)

Also

a₁ + a₄ = 42 ← substitute a₄ = 27

a₁ + 27 = 42 ( subtract 27 from both sides )

a₁ = 15

substitute a₁ = 15 into (1)

15 + 3d = 27 ( subtract 15 from both sides )

3d = 12 ( divide both sides by 3 )

d = 4

User Adam Balsam
by
7.6k points