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PLEASE HELP 20 POINTS

PLEASE HELP 20 POINTS-example-1
User Rmweiss
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1 Answer

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Answer:

S n = n/2 (2 a 1 +d(n-1) )

n=10

Explanation:

4,7,10,.... is an infinite series and Sn for an infinite series is infinity when d>0 or negative infinity when d<0

The formula for the sum of an arithmetic series is given by

S n = n/2 ( a 1 + a n )

and an is found by

an =a1+d(n-1)

Substituting in

S n = n/2 ( a 1 +a1+d(n-1) )

Simplifying

S n = n/2 (2 a 1 +d(n-1) )

Taking the series

4,7,10,.....

a1 =4

7-4 =3

10-7 =3

So d = 3

Sn = 175

175 = n/2 (2*4+3(n-1))

Multiply by 2

175*2 = 2*n/2 (2*4+3(n-1))

350 = n (2*4+3(n-1))

Distribute the 3 and simplify

350 = n(8+3n-3)

350 = n(5+3n)

Distribute the n

350 =5n +3n^2

Subtract 350 from each side

350-350 = 3n^2 +5n -350

0 = 3n^2 +5n -350

Factor

0 = (n - 10) (3 n + 35)


Using the zero product property

n-10 = 0 3n+35=0

n=10 3n=-35

n=-35/3

n cannot be negative


User Iopq
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