Help me find n

Question

If sn=5400, when a₁= 70 and common difference(d)= 10

Answer 1

Start with the sum formula for an arithmetic sequence

 

S_n = (a₁ + a_n)*n/2

 

Now plug in all the information that you have to get

5400 = (70 + a_n)*n/2

 

We still have 2 variables so we need to calculate a_n 0r n

 

So a_n = a₁ + d(n-1) so a_n= 70 + 10n - 10 = 60 + 10n we can now substitute that in to get one variable

5400 = (70 + (60+10n))*n/2

5400 = (130 + 10 n)*n/2

5400 = 65n + 5n²

0 = 5n² + 65n - 5400

0 = n² + 13n - 1080

0 = (n+40)(n-27)

n = -40 or n=27

 

So a₂₇ = 70 + 10(26) = 330

 

Hope this helped.

Answer 2

The explicit form of an arithmetic sequence is:

 

      a_n = a₁ + (n-1)d

 

In your problem we have:

• a_n = 5400
• a₁ = 70
• d = 10

 

      5400 = 70 + (n-1)10

      5400 = 70 + 10n - 10

 

Solve for n