What is the 20th term of the arithmetic sequence 2, –4, –10, … ?

3 Answers
Mar 5, 2018

-112

Explanation:

the nth term of an AP

a,a+d,a+2d,..

is n^(th)=a+(n-1)d

here we have

2,-4,-10,...

a=2

and it is seen that d=-6

:. 20^(th)=2+(20-1)(-6)

=2+19xx-6=2-114

=-112

Mar 5, 2018

20^(th) term =-112

Explanation:

If the sequence is denoted by the series a_i
then a_i=a_(i-1)-6

Setting a_0=8
so that the first term is a_1=2 (as given)

we have a_n=a_0-(n * 6)

For n=20
color(white)("XXX")a_20 = 8- 20*6=8-120=-112

Mar 5, 2018

T_20 = -112

Explanation:

The terms in the sequence 2, -4, -10 ... all differ by -6

You can keep writing the terms until you get to the 20th, but that is not a very mathematical way of doing it and would be VERY time-consuming if you were asked for the 200th term for example.

Find the rule for the sequence... called T_n

If the difference is -6, then the rule starts with T_n = -6n

You need to adjust the rule to start at the correct number,
n starts from 1, 2, 3, 4 ... for each successive term.

When n=1, " "-6(1) = -6

But the first term must be 2 therefore add 8

T_n = -6n+8

Check if n=2
T_2 = -6(2)+8 = -12+8 =-4

Check if n=3
T_3 = -6(3)+8 = -18+8 =-10

Now find the 20th term:

T_20 = -6(20)+8

=-120+8 = -112