Question

Two terms of an arithmetic sequence are t6=-3 and t11=-13. What is t20?

Answer 1

t(6) = -3
t(11) = -13

-3 - (-13) = 10
10/5 = 2

Go one term back from last term to find term 1.

t(10) = 10(2) + -13 = 7

t(1) = 7
Now you can find term 0

7 + 2 = 9
t(0) = 9

Common difference is: d = -2

Equation: tn = -2n + 9

t(1) = 7
t(2) = 5
t(3) = 3
t(4) = 1
t(5) = -1
t(6) = -3
t(11) = -13
t(20) = -31

Answer 2

or, just note that T20 = T11+9d = -13-18=-31

Answer 3

Thank you