Find a(subscript 6) of an arithmetic sequ3nce if a(subscript 4)=5 and a(subscript 9)=20.
The value of an increases 15/5 = 3 per term. Therefore
a4 = 5
a5 = 8
a6 = 11
a7 = 14
a8 = 17
19 = 20
The last term in my previous post should have been labeled a9, not 19.
To find the value of a₆ in an arithmetic sequence, we can use the formula:
aₙ = a₁ + (n - 1) * d
where aₙ represents the nth term in the sequence, a₁ represents the first term, n represents the position of the term, and d represents the common difference between terms.
Given that a₄ = 5 and a₉ = 20, we can substitute these values into the formula to find the common difference:
5 = a₁ + (4 - 1) * d
20 = a₁ + (9 - 1) * d
Simplifying these equations gives us the following system of equations:
a₁ + 3d = 5 ...........(1)
a₁ + 8d = 20 ...........(2)
To solve this system of equations, we can subtract equation (1) from equation (2) to eliminate a₁:
(a₁ + 8d) - (a₁ + 3d) = 20 - 5
8d - 3d = 15
5d = 15
d = 3
Now that we know the common difference, we can substitute it back into equation (1) to find the value of a₁:
a₁ + 3 * 3 = 5
a₁ + 9 = 5
a₁ = -4
Finally, we can use the formula to find a₆:
a₆ = a₁ + (6 - 1) * 3
a₆ = -4 + 5 * 3
a₆ = -4 + 15
a₆ = 11
Therefore, the value of a₆ in the arithmetic sequence is 11.