81.0k views
1 vote
PLEASE HELP 30 POINTS!!

PLEASE HELP 30 POINTS!!-example-1
User Kalten
by
7.7k points

2 Answers

4 votes

Answer:

n=9 and n = 12

User Nicolas Albert
by
8.1k points
3 votes

Answer:

n=9 and n = 12

Explanation:

an = a1 +d(n-1) is the formula for an arithmetic series

The first term is a1 and is 2.5

The 3rd term is

2 =a1 + d(3-1)

2 = 2.5 + 2d

Solve for d

Subtract 2.5 from each side

2-2.5 = 2.5 -2.5 +2d

-.5 = 2d

Divide by 2

-.5/2 = 2d/2

-.25 =d


an = 2.5 -.25(n-1)


The sum is found by using

Sn = n/2 (a1+an)

Sn = 13.5

Substituting the formula for an)

13.5 = n/2 (2.5 + 2.5 -.25(n-1))

Multiply each side by 2 to get rid of the fraction

2*13.5 = 2* n/2 (2.5 + 2.5 -.25(n-1))

27 = n*(2.5 + 2.5 -.25(n-1))

Combine like terms

27 = n*(5- .25(n-1))

Distribute inside the parentheses

27 = n(5-.25n +.25)

Combine like terms

27 = n(5.25-.25n)

Distribute

27 = 5.25n - .25n^2

Subtract 27 on each side

27-27 = 5.25 n - .25 n^2 -27

0 = 5.25 n - .25 n^2 -27

Multiply by -4 so that the coefficient on the x^2 term is 1

0 =-21n +n^2 +108

Rewrite in standard order

0= n^2 -21n +108

Factor

0=(n-9) (n-12)

Using the zero product property

n = 9 and n=12

It Sums to 13.5 twice

When n= 9 and when n=12

Check:

a1 =2.5 a2 =2.25, a3 = 2 a4 = 1.75 a5 = 1.5 a6 = 1.25 a7 = 1 a8=.75

a9 = .5 a10 =.25 a11 =0 a12 = -.25

User Buena
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories