Question

Find a formula for the n-th term, T-n
, of an arithmetic sequence where the 3rd term is 18 and the 8th term is 43.
Hence, or otherwise, find the 20th term of the sequence.

Answer 1

Answer:

nth term is $5n-2$ and 20th term is 98

Step-by-step explanation:

Let us assume the ap as $a,a+d,a+2d...$

B/Q,

$a+3d=18 ...(i)$ and $a+8d=43 ...(ii)$

subtracting (i) from (ii),

$[a+8d]-[a+3d]=[43]-[18]\\=> 8d-3d=25\\=> 5d=25\\=> d=5$

so, putting d=5 in (i) we get,

$a+3(5)=18\\=> a+15=18\\=> a=3$

therfore, nth term = $a+(n-1)d\\= 3+(n-1)5\\= 3+5n-5\\= 5n-2$

hence, 20th term = $5(20)-2=100-2=98$