I'm stuck on this and need help.

Question

Write an equation for the n th term of the arithmetic sequence -5, 0, 5, 10, ...

Then find a_50.

Answer 1

Write an equation for the n th term of the arithmetic sequence −5, 0, 5, 10, ... Then find a₅₀.

Detailed Solution:

Given/Known: a₁ = −5 d = 5 a_n = a₁ + (n − 1)d a_n = ?? a₅₀ = ??

a_n = a₁ + (n − 1)d

a_n = (−5) + (n − 1)(5) = −5 + 5n − 5 = 5n − 10

a_n = 5n − 10 <== Final Solution

a₅₀ = 5(50) − 10 = 250 − 10 = 240

a₅₀ = 240 <== Final Solution

Check the given: −5, 0, 5, 10, ...

a_n = 5n − 10

a₁ = 5(1) − 10 = 5 − 10 = −5

a₂ = 5(2) − 10 = 10 − 10 = 0

a₃ = 5(3) − 10 = 15 − 10 = 5

a₄ = 5(4) − 10 = 20 − 10 = 10

Answer 2

Hello Tigran,

An arithmetic sequence is defined by the equation: a_n=a_1+d*(n-1) where: a_1 is the 1st term and d is the common difference.

Look at the difference between each consecutive terms of the sequence you have: it is always equal to 5. So 5 will be the common difference d.

Now what is the first term of your sequence? It is a_1 = -5

Put that together and you've got your equation: a_n = -5 + 5(n-1) = -5 + 5n -5 = 5n -10

To find a_50, replace n by 50 and you will get the right answer.

Cheers.