Question

the 2nd, 3rd, and 4th term of an arithemetic progression are x-2, 5 and x+2 respectively, calculate the value of x and hence find the 20th term..

Answer 1

since these are consecutive terms, their difference is the same, so

5-(x-2) = (x+2)-5
5-x+2 = x+2-5
7-x = x-3
2x = 10
x = 5

So, the three terms are 3,5,7

So, Tn = 1+2(n-1)
T20 = 1+2(19) = 39

Answer 2

3(19)=39 : 57=39 : 57-39=18