Help me with this asap

a[25]=1.7, d=0.6

In general,

a[n] = a[1] + d(n-1)

1.7 = a[25] = a[1] + 0.6(25 - 1)

a[1] = 1.7 - 0.6(24) = -12.7

a[n] = -12.7 + 0.6(n - 1)

Answer a[1]=-12.7

Filling in the boxes,

a[1]=-12.7, a[2]=-12.1, a[3]=-11.5, a[4]=-10.9, a[5]=-10.3, a[6]=-9.7

check that last one with the formula, a[6]=-12.7-.6(6-1) = -9.7, good

we're asked for a recursive formula, which is easier,

a[n] = a[n-1] + 0.6

a[n] = a[1] + d(n-1)

a[23] = 21 = a[1] + 22d

a[43] = 61 = a[1] + 42d

Subtracting,

40 = 20d

d = 2

21 = a[1] + 22(2)

a[1] = 21 - 44 = -23

a[1] = -23,  a[n] = a[n-1] + 2

Check: a[n]=-23 + 2(n-1) at n=43 gives a[43]=-23 +2(42) =61, good

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'.