# Math

posted by .

The sum of 16terms oe an A.P is -504,while the sum of its 9terms is -126.Find the sum of its 30terms

• Math -

sum of 16 terms is -504 ---> 8(2a + 15d) = -504
2a + 15d = -63

sum of 9 terms is -126 --> (9/2)(2a + 8d) = -126
2a + 8d = -28

subtract:
7d = -35
d=-5
in 2a+8d=-28
2a - 40 = -28
2a = 12
a=6

sum(30) = 15(12 + 29(-5)) = -1995

• Math -

S16 = 16/2 * (2a+15d) = -504
S9 = 9/2 * (2a + 8d) = -126

16a + 120d = -504
9a + 36d = -126

Multiply #1 by 9 and #2 by 16, then subtract:

144a + 1080d = -4536
144a + 576d = -2016

504d = -2520
d = -5
a = 6

S30 = 15(2a+29d) = 15(12 - 145) = -1995

• Math -

-1995

## Similar Questions

1. ### Precalculus

Find the sum of the first 50 terms of the sequence 2,4,6,8........ That is twice the sum of 1+2+3+...+50 For 1+2+...+N, the sum is N(N+1)/2 The sum is therefore 2*[50*51)/2) = 2550
2. ### math

Find the two numbers that multiply to the product number and add to the sum number of the following: a)Product 563033256; Sum 51895 b)Product -43481220; Sum 28429 c)Product 2545124358; Sum -105619 I tried xy = product and x+y = sum, …
3. ### calculus

find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is?
4. ### calculus

Find the sum of the series (-1)^n (5^(2n))/n! 1. sum = e^25 2. sum = e^−5 3. sum = 5 4. sum = e^5 5. sum = 25 6. sum = e^−25
5. ### Math

Sum of4th and the 6th terms of an a,p is 42 . While the sum of the 3rd and 9th terms of the same a.p is 52. Find the (a) first term (b)common difference (c) sum of the first ten terms of the progression. Solution
6. ### math URGENT!!!!

i have a list of 5 different numbers. the sum of 2 of the numbers is 0. the sum of 2 of the numbers is 1. the sum of 2 of the numbers is 2. the sum of 2 of the numbers is 3. the sum of 2 of the numbers is 4.the sum of 2 of the numbers …
7. ### probability

two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability …
8. ### Maths

John, Amos and Peter shared the sum of #126 in the proportiom 1: 2: 4, find the sum of money each received.
9. ### maths

Sum of first 30terms of an a.P. are equal to first 20 terms.show that the sum of first 50terms of the same ap is zero
10. ### Math3c

1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find …

More Similar Questions