in an arithmetic sequence a1=4 and d=8 which term is 428
Show your work
term(n) = a + (n-1)d
428 = 4 + (n-1)(8)
424 = 8n - 8
432 = 8n
n = 54
Draw your conclusion
S8 = 8/2 [2(A1) + (8 - 1)3]
172 = 8/2 [2A1 + (7)3]
172 = 8/2 (2A1 + 21)
344 = 8 (2A1 + 21)
344 = 16A1 + 168
344 - 168 = 16A1
11 = A1
To find out which term in the arithmetic sequence has a value of 428, you can use the formula for the nth term of an arithmetic sequence.
The nth term formula is:
an = a1 + (n - 1)d
Given:
a1 = 4
d = 8
We need to find the value of n when an = 428.
428 = 4 + (n - 1)(8)
Let's solve for n:
428 = 4 + 8n - 8
428 - 4 + 8 = 8n
432 = 8n
n = 432 / 8
n = 54
Therefore, the term with a value of 428 is the 54th term in the arithmetic sequence.
To find the term in an arithmetic sequence, we use the formula:
an = a1 + (n-1)d
Where:
an = the nth term
a1 = the first term
d = the common difference between terms
n = the term number we want to find
Given that a1 = 4 and d = 8, we need to find the value of n when an = 428.
428 = 4 + (n-1)8
Now, we can solve this equation for n.
428 = 4 + 8n - 8
Simplifying further:
428 - 4 + 8 = 8n
432 = 8n
Dividing both sides by 8:
n = 54
Therefore, the term number 54 is 428 in the given arithmetic sequence.