Final answer:
The arithmetic sequence with a first term of 11/8 and a common difference of 1/2 is found using the formula an=a1+(n-1)d. a23 is calculated to be 11/4, and the first 5 terms are 11/8, 15/8, 19/8, 35/8, and 27/8.
Step-by-step explanation:
To find the arithmetic sequence with a first term of 11/8 and a common difference of 1/2, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
Substituting the given values, we have:
an = 11/8 + (n-1)(1/2)
To find a23, we substitute n = 23:
a23 = 11/8 + (23-1)(1/2) = 11/8 + 22(1/2) = 11/8 + 11 = 22/8 = 11/4
To find the first 5 terms, we substitute n = 1, 2, 3, 4, and 5 into the given formula:
a1 = 11/8 + (1-1)(1/2)
= 11/8
a2 = 11/8 + (2-1)(1/2)
= 11/8 + 1/2
= 15/8
a3 = 11/8 + (3-1)(1/2)
= 11/8 + 1
= 19/8
a4 = 11/8 + (4-1)(1/2)
= 11/8 + 3/2
= 35/8
a5 = 11/8 + (5-1)(1/2)
= 11/8 + 2
= 27/8