The fourth term of an arithmetic sequence is 18 and the sixth term is 28. Give the first 3 terms
Use your arithmetic formula to get two equations in two unknowns : )
tn= a + (n-1)d
t4 = a + (4-1)d
while t4=18
18 = a + 3d
and t6 = 28
so
28 = a + (6-1)d
and then just solve the two equations in two unknowns, and I would be happy to check your solution : )
Did you solve it ?? : )
the 4th and 6 terms differ by 2d
so, 2d=10
and the rest is a cinch.
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right?
To find the first 3 terms of an arithmetic sequence, we need to determine the common difference (d) first, which represents the difference between consecutive terms.
We are given that the fourth term (a₄) is 18 and the sixth term (a₆) is 28. Using this information, we can find the common difference as follows:
a₄ = a₁ + 3d (since a₄ is the fourth term, three terms have been skipped)
18 = a₁ + 3d
a₆ = a₁ + 5d (since a₆ is the sixth term, five terms have been skipped)
28 = a₁ + 5d
Solving this system of equations, we can eliminate a₁ and solve for d:
Subtracting the first equation from the second equation:
28 - 18 = (a₁ + 5d) - (a₁ + 3d)
10 = 2d
d = 10/2
d = 5
Now that we know the common difference (d = 5), we can find the first term (a₁) by substituting the value of d into any of the equations:
18 = a₁ + 3(5)
18 = a₁ + 15
a₁ = 18 - 15
a₁ = 3
Therefore, the first three terms of the arithmetic sequence are 3, 8, and 13.