Question #46f4b

2 Answers
Jun 22, 2016

286.8 is the 24th term in the sequence.

Explanation:

In an arithmetic sequence we need to know a and daandd.
We know neither of them, and as we are looking for two variables, we will make simultaneous equations.
T_n = a + (n-1)dTn=a+(n1)d

For T_5:" " 47.4 = a + 4d " "AT5: 47.4=a+4d A
ForT_10:" " 110.4 = a + 9d " B"T10: 110.4=a+9d B

B-A : " "63 = 5d 63=5d
" " d = 12.6 d=12.6

Substitute 12.6 for d in A:

" " 47.4 = a + 4 xx 12.6 47.4=a+4×12.6
" "47.4 - 50.4 = a 47.450.4=a

a = -3a=3

Now we can write the General Term for this sequence..
T_n = -3 + (n-1)12.6Tn=3+(n1)12.6

Which term is 286.8??

-3 + (n-1)12.6 = 286.83+(n1)12.6=286.8
-3 + 12.6n -12.6 = 286.83+12.6n12.6=286.8
12.6n = 302.412.6n=302.4
n = 24n=24

Jun 22, 2016

"The term number for 286.8 is "T_24The term number for 286.8 is T24

Explanation:

Let the number of steps be ss
Let the 5th term be aa
Let the difference between terms be kk

color(blue)("Determine the difference between terms.")Determine the difference between terms.

An arithmetic sequence is of form:

a"; "a+k"; "a+2k"; "a+3k"; ........"a; a+k; a+2k; a+3k; ........

The number of steps between the given terms:

T_5, T_6, T_7, T_8, T_9, T_10T5,T6,T7,T8,T9,T10

So there are 5 steps from T_5T5 to T_10=>s=5T10s=5

=>T_5+5k=T_10T5+5k=T10

color(brown)(=>k=(T_10-T_5)/5)color(blue)(" "->" "k=(110.4-47.4)/5=63/5k=T10T55 k=110.447.45=635
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thus for the target term we have:
color(brown)(T_5+sk=286.8" "color(blue)(->" "47.4+63/5s=286.8T5+sk=286.8 47.4+635s=286.8

=>s=(5(286.8-47.4))/63s=5(286.847.4)63

s=19" steps from "T_5s=19 steps from T5

So the term is T_(5+19)=T_24T5+19=T24