The 31st term of the arithmetic progression is 98.
The Breakdown
The formula for the nth term of an AP is given by:
an = a1 + (n - 1) × d
Where:
an = nth term of the AP
a1 = first term of the AP
n = position of the term in the AP
d = common difference between consecutive terms
Given that the first term (a1) is 8 and the last term (an) is 185, we can find the common difference (d) using the formula:
an = a1 + (n - 1) × d
185 = 8 + (60 - 1) × d
185 = 8 + 59d
177 = 59d
d = 177 / 59
d = 3
Now that we have the common difference (d), we can find the 31st term (a31) using the formula:
a31 = a1 + (31 - 1) × d
a31 = 8 + 30 × 3
a31 = 8 + 90
a31 = 98
Therefore, the 31st term of the arithmetic progression is 98.