Question

А3=-11;а16=-56 а1-?,d-?

Answer 1

A3=a1+2d=-11
a16=a1+15d=-56
d=-5 a1=-1

Answer 2

To find the first term (a1) and the common difference (d) of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1) * d

Where: an is the nth term, a1 is the first term, n is the term number, d is the common difference.

Given that a3 = -11 and a16 = -56, we can use these two pieces of information to set up two equations and solve for a1 and d.

1. Using a3: a3 = a1 + (3 - 1) * d -11 = a1 + 2d

2. Using a16: a16 = a1 + (16 - 1) * d -56 = a1 + 15d

Now we have a system of two equations with two variables. We can solve it to find the values of a1 and d.

Let's solve the system of equations:

1. -11 = a1 + 2d
2. -56 = a1 + 15d

We can use the method of substitution or elimination to solve the system. Let's use the method of elimination:

Multiply the first equation by 15 and the second equation by 2 to make the coefficients of 'd' the same and then subtract the equations to eliminate 'd'.

15 * (-11) = 15a1 + 30d 2 * (-56) = 2a1 + 30d

-165 = 15a1 + 30d -112 = 2a1 + 30d

Now, subtract the second equation from the first:

(-165) - (-112) = 15a1 - 2a1 -165 + 112 = 13a1 -53 = 13a1

Now, solve for a1:

a1 = -53 / 13 ≈ -4.08 (rounded to two decimal places)

Now that we have a1, we can substitute it back into either of the original equations to solve for 'd'. Let's use the first equation:

-11 = a1 + 2d -11 = (-4.08) + 2d -11 + 4.08 = 2d -6.92 = 2d

Now, solve for 'd':

d = -6.92 / 2 ≈ -3.46 (rounded to two decimal places)

So, the first term (a1) is approximately -4.08 and the common difference (d) is approximately -3.46.