How do you write the expression for the nth term of the sequence given 1,4,7,10,13,...?

Question

siriceboynu1 · Accepted Answer

We should recognise that 1,4,7,10,13.... is an A.P. with a common difference of 3.d=3The expression for the nth term can be determined from the formula, but there is a short cut.            T      n        =    d    ×    n    +    ?    ?    ?  As soon as see that d=3, you will know that the expression for the nth term with start with             T      n        =    3    n  Now you just have find what must be added or subtracted to start at the correct first term.Let       n    =    1                                →    3    ×    1    =    3    ,                     but                     T      1       must be 1, so subtract 2Let       n    =    2                                →    3    ×    2    =    6                     but                     T      2       must be 4. so subtract 2It would seem that the expression we want is:             T      n        =    3    n    -    2  Check with             T      3       which must be 7.      3    ×    3    -    2    =    7              T      n        =    3    n    -    2  Using the formula :             T      n        =    a    +          (      n      -      1      )        d  In 1,4,7,10,14,...      a    =          T      1        =    1                     and                    d    =    3              T      n        =    1    +          (      n      -      1      )        ×    3                                   ←   simplify            T      n        =    1    +    3    n    -    3              T      n        =    3    n    -    2

Rhett Guerrero · Accepted Answer

1;4;7;10;13;........... is an arithmetic series            n      1        =    1   and the common difference, d=3      ∴                 nth term        =    1    +          (      n      -      1      )        ⋅    3

How do you write the expression for the nth term of the sequence given 1,4,7,10,13,...?

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