Find a6 for an arithmetic sequence where a1=3x+1 and d=2x+6 . I can't even solve it because I do not have any idea.
in an arithmetic sequence
term(n) = a + (n-1)d
inyour case a = 3x+1
d = 2x+6
term(6) = a + 5d
= 3x+1 + 5(2x+6)
= 3x+1 + 10x + 30
= 13x + 31
To find the sixth term, a6, of an arithmetic sequence, we need to use the given information about the first term, a1, and the common difference, d.
Given:
a1 = 3x + 1
d = 2x + 6
An arithmetic sequence has a constant difference between each term, which means that we can find any term by adding the common difference to the previous term.
The formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
To find a6, we substitute n = 6 into this formula and solve:
a6 = a1 + (6 - 1)d
= a1 + 5d
Substituting the given values for a1 and d:
a6 = (3x + 1) + 5(2x + 6)
Now, let's simplify the expression:
a6 = 3x + 1 + 10x + 30
= 13x + 31
Therefore, the sixth term of the arithmetic sequence is 13x + 31.
To find the value of a6 for an arithmetic sequence, we first need to find the formula for the nth term (an) in terms of the first term (a1) and the common difference (d).
The formula for the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d
Given that a1 = 3x + 1 and d = 2x + 6, we can substitute these values into the formula to find a6.
a6 = a1 + (6-1)d
a6 = (3x + 1) + (5)(2x + 6)
a6 = 3x + 1 + 10x + 30
a6 = 13x + 31
Therefore, a6 = 13x + 31.