Question #46f4b

2 Answers
Jun 22, 2016

Answer:

286.8 is the 24th term in the sequence.

Explanation:

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

For #T_5:" " 47.4 = a + 4d " "A#
For#T_10:" " 110.4 = a + 9d " B"#

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

Substitute 12.6 for d in A:

#" " 47.4 = a + 4 xx 12.6#
#" "47.4 - 50.4 = a#

# a = -3#

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

Which term is 286.8??

#-3 + (n-1)12.6 = 286.8#
#-3 + 12.6n -12.6 = 286.8#
#12.6n = 302.4#
#n = 24#

Jun 22, 2016

Answer:

#"The term number for 286.8 is "T_24#

Explanation:

Let the number of steps be #s#
Let the 5th term be #a#
Let the difference between terms be #k#

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

An arithmetic sequence is of form:

#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_10#

So there are 5 steps from #T_5# to #T_10=>s=5#

#=>T_5+5k=T_10#

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

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

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

#s=19" steps from "T_5#

So the term is #T_(5+19)=T_24#