# maths

The sum of first 6 terms of an Arithmetic progression is 6 the product of 2nd term and 5th term is -80 . Find the terms of A.P.

1. 👍 0
2. 👎 0
3. 👁 388
1. sum of first 6 terms
= (6/2)(2a + 5d) = 6
2a + 5d = 2 ---> a = (2-5d)/2 **

(a+d)(a+4d) = -89
a^2 + 5ad + 4d^2 = -80
sub ** into that
(2-5d)^2/4 + 5d(2-5d)/2 + 4d^2 = -80
times 4, the LCD
(2-5d)^2 + 10d(2-5d) + 16d^2 = -320
4 - 20d + 25d^2 + 20d - 50d^2 + 16d^2 + 320 = 0
-9d^2 + 324 = 0
d^2 = 36
d = ± 6

if d = 6, a = (2 - 30)/2 = -14
terms are: -14, -8, -2, 4, 10, 16, ....

you do the case when d = -6

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

The third,sixth and seventh terms of a geometric progression(whose common ratio is neither 0 nor 1) are in arithmetic progression. Prove dat d sum of d first three is equal to d fourth term

2. ### Arithmetic

The sum of three consecutive terms of a geometric progression is 42, and their product is 512. Find the three terms.

3. ### maths

the sum of the 4th and 6th terms of an A.P is 42. the sum of the 3rd and 9th terms of the progression is 52. find the first term, the common difference and the sum of the first ten terms of the progression.

4. ### Math, Series

Given that 1/(y-x), 1/2y, and 1/y-z are consecutive terms of an arithmetic progression, prove that x,y, and z are consecutive terms of a geometric progression.

1. ### Arithmetic

The first, second and third terms of a geometric progression are 2k+3, k+6 and k, respectively. Given that all the terms of geometric progression are positive, calculate (a) the value of the constant k (b) the sum to infinity of

2. ### Maths

The numbers p,10 and q are 3 consecutive terms of an arithmetic progression .the numbers p,6 and q are 3 consecutive terms of a geometric progression .by first forming two equations in p and q show that p^2-20p+36=0 Hence find the

3. ### Mathematics

The 2nd,3rd and 4th term of an arithmetic progression are x-1,5,x+2 respectively calculate the value of x.

4. ### Mathematics

If the sixth term of an arithmetic progression (A.P) is 37 and the sum of the six term is 147, find the first term, common difference, sum of the first fifteen terms

1. ### math

There are two positive numbers that can be inserted between 3 and 9 such that the first three are in geometric progression while the last three are in arithmetic progression. Find the sum of those two numbers.

2. ### AP calculus

The sixth term of an Arithmetic Progression is 23 and the sum of the six terms is 78. Find the first term and the common difference.

3. ### MATH

three consecutive terms of a geomentric progression series have product 343 and sum 49/2. fine the numbers. HOW WILL ONE SOLVE THAT? THANKS

4. ### mathematics

In a geometric progression with terms, the sum of the first and last term is 66 and the product of the second and second last term is 128. Given that the sum of all the terms of this geometric progression is 126, find the number