Find the first term and the common difference of the arithmetic sequence whose 7th term is 30 and 14th term is 65

Question

this question asks me

First term is ?

common difference?

Please help thank you

Answer 1

Use the formula a_n = a₁ + (n-1)d with n = 7 and n = 14 to get:

30 = a₁ + 6d

65 = a₁ + 13d

Then solve for a₁ and d.

Answer 2

desmos.com/calculator/qoiafg1isl

Try enabling f(x) in the above graph to see that an arithmetic sequence is similar to a function, but with a discreet domain (natural numbers).