Question

Find a formula for the n-th term, Tn, 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:

Hey, refer to attach images for answer

A20=103

Tn=5n+3

Answer 2

Answer:

Given

Solutin

d =  ( Tk-Tj ) /( k-j)     k>j

d =  ( T8 -T3  )/( 8-3)  =( 43-18 )/( 5)  

d=25/5=5

As  Tn=a+(n-1)d

Here n=3 , and d =  5

By putting these , we get  

T3=a+2 d

18  =a+2 (5)

=>  a= 18 -10 = 8

So the arithmetic series will becomes  

8 , 13, 18 ,…..

If we find T_20= ??

T_20=8+19*5=  103     Ans  

Solutin

d =  ( T_k-T_j  )/( k-j)     k>j

d =  ( T_8-T_3  )/( 8-3)  =( 43-18 )/( 5)  

d=25/5=5

As  T_n=a+(n-1)d

Here n=3 , and d =  5

By putting these , we get  

T3=a+2 d

18  =a+2 (5)

=>  a= 18 -10 = 8

So the arithmetic series will becomes  

8 , 13, 18 ,…..

If we find T20= ??

T20=8+19*5=  103    Ans