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September 16, 2014

September 16, 2014

Posted by **said** on Thursday, June 16, 2011 at 4:51am.

B) in an A.P,the sum of the first five term is 30, and the third term is equal to the sum of the first two. Write the first five terms of the progression.

- math-G.P and A.P -
**Reiny**, Thursday, June 16, 2011 at 8:21amA)

a=5, d=5 , n = ? , Sum(n) ≥ 400 000

(n/2)(10 + (n-1)(5)) ≥ 400 000

n(5n + 5) ≥ 800 000

5n^2 + 5n - 800 000 ≥ 0

n^2 + n - 160 000 ≥ 0

Now I took √160000 = 400

so if the above had been

n^2 + n - 159999 it would have factored to

(n+401)(n-399)

so our equation must have a solution between 399 and 401.

Since n must be a whole number,

sum(399) = (399/2)(10 + 398(5)) = 399000

sum (400) = (400/2)(10 + 399(5)) = 399200

sum(401) = (401/2)(10 + 400(5)) = 403005

So you need 401 terms to exceed 400000

B) "the sum of the first five terms is 30" ---> (5/2)(2a + 4d) = 30

2a + 4d = 12

a + 2d = 6

"the third term is equal to the sum of the first two" ---> a+2d = a + a+d

a = d

sub that into first equation:

d + 2d = 6

d = 2 , then a = 2

first 5 terms: 2 , 4 , 6, 8, and 10

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