the sum of the first 10 terms in the sequence is 362.5.
Step-by-step explanation: Find a -10 Using the recursive formula a,n=a,n−1−2.5 you can calculate a,10 by repeatedly applying this formula:
a2=a1−2.5=22.5
a3=a2-2.5=22.5-2.5=20
a4=a3-2.5=20-2.5=17.5
Continuing this pattern:
a10=a9-2.5
a10=5-2.5=25
So, a10=25
Find the sum of the first 10 terms in the sequence:
To find the sum of the first 10 terms of an arithmetic sequence, you can use the formula for the sum of an arithmetic series: Sn=n/2(2a1+(n-1)d)
Sn represents the sum of the first n terms.
a1 is the first term of the sequence, which is 25.
n is the number of terms, which is 10.
d is the common difference, which is -2.5.
Then you plug these values into the formula:
S10=10/2(2x25+(10-1)x(-2.5))
S10=5(50+22.5)
S10=5x72.5
S10=362.5