two terms of an arithmetic sequence are t5=-31.4 and t10=-50.4. what is t23?

Question

anonymous · Answer

t10-t5 equal -19,  10-5=5  so t, -19/5=-3.8, is t1 so t32 is -3.8times 32

anonymous · Answer

when I multiply -3.8 to 32, I come up with -121.6 

but -121.6 isn't one of the given choices

anonymous · Answer

should be t10+t5

campbell_st · Answer

set up 2 equations using the formula for a term in an AP

$$a_{n} = a + (n - 1)d$$

a = 1st term, n = number of terms, d = common difference


so solve simultaneously


term 10:                a + 9d = -50.4             equation 1
term  5                  a + 4d = -31.4             equation 2
                            ---------------
eq 1 - 2                      5d = -19

so the common difference is d = -3.8

substitute into either equation to find the 1st term 


when you get that you can use the formula above to find the 23 term, n = 23

amistre64 · Answer

an arithmetic sequence is a discrete form of a line ....

you are given 2 points to define the line with