Question

is 205 in this sequence 1,5,9,13

Answer 1

Answer: Yes

Explanation:

a=1,a2=5,a3=9,a4=13

d1=a2-a1=5-1=4

d2=a3-a2=9-5=4

d4=a4-a3=13-9=4

d1=d2=d3.

So,given series is an A.P.

So common difference=d=4.

let 205 is nth term of AP

Since,an=a+(n-1)d

205=1+(n-1)4

205-1=(n-1)4

204/4=n-1

51+1=n

n=52.

So 205 lies in this sequence.

and also it is 52th term