the 4th term of an ap is equal to 3 times the first term and the 7th term exceeds twice the third term by 1 find the first term and the common difference

We're given

a₄ = 3a₁

a₇ = 2a₃ + 1

Since these numbers form an arithmetic progression, we have for some fixed constant d

a₂ = a₁ + d

a₃ = a₂ + d = a₁ + 2d

a₄ = a₃ + d = a₁ + 3d

and so on, up to

a₇ = a₁ + 6d

Rewrite the given equations in terms of a₁, then solve for a₁ and d :

a₁ + 3d = 3a₁

a₁ + 6d = 2 (a₁ + 2d) + 1

2a₁ - 3d = 0

a₁ - 2d = -1

(2a₁ - 3d) - 2 (a₁ - 2d) = 0 - 2 (-1)

2a₁ - 3d - 2a₁ + 4d = 0 + 2

d = 2

a₁ + 3d = 3a₁

3 (2) = 2a₁

a₁ = 3

76%

step-by-step explanation:

24% are dogs and the remaining is 76% because 100-24=76

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.