2021-08-19

Complete the following quenstions involving definitions for sequences
Whitch of the following sequences is being generated by an "Explicit Formula"?
1)${a}_{n}=\left\{{n}^{2}+3\right\}$
2)${a}_{n}=\left\{{5}_{n}+7\right\}$
3)${a}_{n}=\left\{\frac{2}{n+1}\right\}$
4)${a}_{n+2}=\left\{{a}_{n}+1-3{a}_{n}\right\}$

2k1enyvp

Explicit Formula:defines the terms of the sequence using their position in the sequence.
i.e. if we put values of n=1,2,3..... in the formula, we can get all terms of sequence.
1)${a}_{n}=\left\{{n}_{2}+3\right\}$

Therefore we are getting sequence 4,7,12,19,....... This is ecplicit formula
2)${a}_{n}={5}_{n}-7$

$n=3,{a}_{3}=8$
Therefore it is sequence generated by explicit formula sequence is −2,3,8,......
3)${a}_{n}=\frac{2}{n+1}$

Therefore we can get all terms of sequence by this formula and hence it is explicit formula. Sequnce is 1,$\frac{2}{3}$,2,........
4)${a}_{n}+2={a}_{n}+1-3{a}_{n}$

Since we cannot find terms from this formula by putting values of n
Therefore this is not explicit formula.

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