Let a sub n be a sequence such that the sum of the first 10 terms is 160 and the sum of the next 10 terms is 340. What is first term?

Question

Show me the solutions of that particular problem

 

Answer 1

For the first half:

160 = (10/2)(2a₁ + 9d)

32 = 2a₁ + 9d        you can verify

 

For the second half:

340 = (10/2)(2a₁₁ + 9d)

68 = 2a₁₁ + 9d       you can verify

 

Creating a system

68 = 2a₁₁ + 9d

32 = 2a₁ + 9d

 

18 = a₁₁ - a₁     Subtract bottom from top and simplify

Recall a₁₁ = a₁ + 10d

18 = a₁ + 10d - a₁     substitute

18 = 10d

1.8 = d

 

Now substitute 1.8 for d into either opening equations.

You should get 

a₁ = 7.9