Monday

December 22, 2014

December 22, 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

**Answer this Question**

**Related Questions**

math - the fourth term of an arithmetic progression is equal to 3 times the ...

math - A geometric series has first term 8 and third term 20 what does the fifth...

math - The sum of the first 10 terms of an arithmetic series is 145 and the sum ...

math - An arithmetic series has a first term 8 and third term 20. What does the ...

Math - The sum of the first seventeen terms of an arithmetic series is 493 The ...

Math - 3,5,-5... The first term in the sequence of #'s shown above is 3. Each ...

math - In a Geometric progression the sum of its first 4 term is equal 15, and ...

arithmetic - The 8th term of an A P is 5times the third term while the 7th term ...

Precalculus - The 8th term in an arithmetic sequence is 5, and the sum of the ...

math - The third term of a G.P is 24 and the sum of the first two terms is 288. ...