Arithmetic Sequence

[lapis elbow]

Hello! I am working on some practice tests, and I encountered this. I already tried to find it using the long way...

[fast shard]

,rccw

[fast shard]

,rccw

[fast shard]

$T_8 =22$

[cyan path]

bettim

[fast shard]

$T_22 = 84$

$T_{22} = 84$

[cyan path]

bettim

[fast shard]

so

$a+(8-1)d=22$

[cyan path]

bettim

[fast shard]

$a+(22-1)d=84$

[cyan path]

bettim

[fast shard]

solving further

$a+7d=22$

[cyan path]

bettim

[fast shard]

$a+21d=84$

[cyan path]

bettim

[fast shard]

sbutracting

$14d=62$

[cyan path]

bettim

[fast shard]

so

,calc 62/14

[cyan path]

Result:

4.4285714285714

[fast shard]

$d=\frac{31}{7}$

[cyan path]

bettim

[fast shard]

so then

$a=-9$

[cyan path]

bettim

[fast shard]

now solve for the 15th term

[sour marsh]

there’s two ways to solve it

one is the long way and one is the short way

[lapis elbow]

It says 53 though? But it's not in the choices

[fast shard]

$a+14d$

[cyan path]

bettim