Question

write the algebraic form of the arithmetic sequence 12,16,20,24,?​

Answer 1

Answer:

(a) Arithmetic sequence is 8,11,14,....

First term, a=8 and common difference, d=11−8=3

Thus, nth term of the sequence is

t  

n

​

=a+(n−1)d=8+(n−1)3=8+3n−3=3n+5

Thus, the  algebraic form of the given arithmetic sequence is 3n+5

(b) Consider the number 121

Therefore, 121=3n+5

⇒ 121−5=3n

⇒ 3n=116

Here, 116 is not divisible by 3

∴ 121 is not a term of the sequence.  

(c) Square of nth term =(3n+5)  

2

=9n  

2

+30n+25=(9n  

2

+30n+25)+5

9n  

2

 term and 30n term are divisible by 3 but 20 is not divisible by3. Hence, the square of the nth term will not occur in this sequence.

Step-by-step explanation: