Question

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

Answer 1

`-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`

Answer 2

`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`

Answer 3

`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`