Question

the 41st term of the arithmetic sequence is -539 and the 54th term is -708. Find the value of the 80th term

Answer 1

`a _(n) = a _(1) + (n - 1)d \\ a _(41) = - 534 \\ a _(54) = - 708 \\ a _(41) = a _(1) + (41 - 1)d = - 534 \\ a _(1) + 40d = - 534 \: \: ...(1)\\ a _(54) = a _(1) + (54 - 1)d =- 708 \\ a _(1) + 53d = - 708 \: \: ...(2)`

Try to solve the similtanious equation to find the first term and the common difference, then use that information to figure out the 80th term... Update me if you need further help ...