Answer:
look down
Explanation:
To find the sum of the first 25 terms of an arithmetic sequence, we can use the formula:
Sn = (n/2)(a1 + an)
Where:
Sn is the sum of the first n terms
n is the number of terms
a1 is the first term
an is the nth term
In this case, a1 = 100 and a25 = 220, so we need to find the value of n and an.
The formula to find the nth term (an) of an arithmetic sequence is given by:
an = a1 + (n - 1)d
Where d is the common difference.
We can calculate d using the values of a1 and a25:
d = (a25 - a1) / (25 - 1)
= (220 - 100) / (25 - 1)
= 120 / 24
= 5
Now, we can find the value of an:
an = a1 + (n - 1)d
220 = 100 + (25 - 1)5
220 = 100 + 24 * 5
220 = 100 + 120
220 = 220
The value of an is 220, which means the 25th term of the sequence is 220.
Now, substituting the values into the sum formula:
Sn = (n/2)(a1 + an)
= (25/2)(100 + 220)
= (25/2)(320)
= 25 * 160
= 4000
Therefore, the sum of the first 25 terms of the arithmetic sequence is 4000.