SOLUTION: Find the 20th term of the AP: 80, 75, 70,…and calculate the number of terms required to make the sum equal to zero

Question 1132827: Find the 20th term of the AP: 80, 75, 70,…and calculate the number of terms required to make the sum equal to zero
Answer by Alex.33(110) (Show Source): You can put this solution on YOUR website!
We have
1.It is arithmetic sequence
2.the first 3 terms 80, 75, 70
We want
1.the 20th term
2.the number n, for which the sum of the sequence S(n)=0
Approach:
1.the general formula of the nth term: a(n)
2.plug n=20 in=>1.
3.the general formula for the sum of the first n terms: S(n)
4.set S(n)=0 and solve.

the common difference: -5
the first term: 80
a(n)=80+(-5)*(n-1)=85-5n

a(20)=-15=>the twelfth term

S(n)=(80+a(n))*n/2=0
n=33=>the number of terms required to make the sum equal to zero
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