Question

In two or more complete sentences, explain whether the sequence is finite or infinite. Describe the pattern in the sequence if it exists and if possible find the sixth term. 2a,2a2b,2a3b2,2a4b3...?

Answer 1

Answer with explanation:

The given pattern is →→2 a,2 a 2 b,2 a 3b²,$2a 4b^3,2a 5b^4....$?

If you will look at the sequence,

First term =2a×$b^0$

Second term =2a×2b

Third term =2a×3b²

Fourth term =2a×4b³

Fifth term =2a ×$5b^4$

Sixth term =2a×$6b^5$

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→2 a is first part of the sequence which is constant in each term,and second part of the sequence is given by $nb^{n-1}$

So, we can say with Surety, this is a sequence.

⇒If you will look at the sequence, power of b increases, in each term by a value of 1.

⇒Since ,natural number are uncountable,So the following sequence is Uncountable that is a infinite Sequence.