Question

. Find at least 3 different sequences beginning with the terms 3, 5, 7 whose terms are generated by a simple formula.

Answer 1

here, we need to figure out 3 different sequences whose first three terms are 3 , 5 , 7 respectively.

there can be infinite number of sequence following the conditions.

in all the cases, suppose the sequence is denoted by {}

FIRST SEQUENCE BE:-

here, we see that 3 , 5 and 7 all are prime numbers.so, the sequence can be all prime numbers starting from 3.hence the sequence is denoted as:-

= {all prime numbers starting from 3}

= { 3 , 5 , 7, 9, ........}

SECOND SEQUENCE BE:-

here, we see that 3 , 5, 7 all are odd numbers.so, the sequence be odd numbers starting from 3.hence the sequence is denoted as:-

= { 2n +1 } ,

putting n=1 we get, a₁ = (2*1 + 1) = 3

n=2 we get , a₂ = (2*2 + 1) = 5

n=3 we get , a₃ = (2*3 + 1) = 7 and so on..

THIRD SEQUENCE BE:-

here we see that when 3 is increased by 2 we get 5...when 5 is increased by 2 then we get 7 ...so , our sequence can be:-

, for all n >1 and = 3

putting n=2, we have, = + 2

= 3+2

= 5

putting n=3, we have, = + 2

= 5+2

= 7 and so on...

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