put these sequences in standard form
arithmetic a1=a6=11
To put a sequence in standard form, we need to identify the common difference (d) between terms.
In the case of an arithmetic sequence, the common difference (d) is the same between every pair of consecutive terms.
Given that a1 = a6 = 11, we can find the common difference as follows:
a1 = a + 0d = 11 ...(1)
a6 = a + 5d = 11 ...(2)
Subtracting equation (1) from equation (2), we get:
a6 - a1 = (a + 5d) - (a + 0d)
11 - 11 = a + 5d - a
0 = 5d
We obtain 0 = 5d, which means the common difference (d) is zero.
When the common difference is zero, it implies that all the terms in the sequence are equal. Therefore, the sequence is a constant sequence, and the standard form would be a = 11.