Question

What is a21 of the arithmetic sequence for which a7 = -19 and a10 =-28

Answer 1

`a_(n) = a_(1) + (n - 1)d \\ a_(7) = a_(1) + (7 - 1)d \\ a_(7) = a_(1) + 6d \\ a_(10) = a_(1) + 9d`

`- 19 = a_(1) + 6d \\ - 28 = a_(1) + 9d \\ \\ - 19 = a_(1) + 6d \\ 28 = - a_(1) - 9d \\\ - 3d = 9 \\ d = - 3`

`a_(1) = - 19 - 6d = - 19 - 6( - 3) = - 1 \\`

`a_(21) = a_(1) + (21 - 1)d \\ a_(21) = - 1 + 20( - 3) = - 61`