3.(i) Is 68 a term of the A.P. 7,10,13,… ?
3.(i) Is 68 a term of the A.P. 7,10,13,… ?

(ii) Is 302 a term of the A.P. 3,8,13, …. ?

An arithmetic progression or arithmetic sequence is a number’s sequence such that the difference between the consecutive terms is constant.

Solutions:

(i) Given, A.P. 7,10,13

Here, a=7 and d={{a}_{2}}-{{a}_{1}}=10-7=3

We know that, {{n}^{th}} term {{a}_{n}}=a+\left( n-1 \right)d

Required to check nth term {{a}_{n}}=68

a+\left( n-1 \right)d=68

7+\left( n-1 \right)3=68

7+3n-3=68

3n+4=68

3n=64

n=64/3 which is not a whole number.

Therefore, 68 is not a term in the A.P.

(ii) Given, A.P. 3,8,13,

Here, a=3 and d={{a}_{2}}-{{a}_{1}}=8-3=5

We know that, {{n}^{th}} term {{a}_{n}}=a+\left( n-1 \right)d

Required to check {{n}^{th}} term {{a}_{n}}=302

a+\left( n-1 \right)d=302

3+\left( n-1 \right)5=302

3+5n-5=302

5n-2=302

5n=304

n=304/5, which is not a whole number.

Therefore, 302 is not a term in the A.P.