what is the sum of the first 12 terms of the arithmetic sequence whose nth term is given by 3n - 2

Question

anonymous · Answer

@amistre64 and @sambhav__jain  here pls

parthkohli · Answer

$$a_1 = 1$$$$a_2 = 4$$$$a_3 = 7$$$$a_4 = 10$$Some nice stuff happening?

harsimran_hs4 · Answer

or
$$\sum_{1}^{10}  (3n  - 2)$$ 
$$3 \sum_{1}^{10} n - \sum_{1}^{10} 2$$

anonymous · Answer

how's that?

amistre64 · Answer

"first twelve terms" is ambiguous and needs to be clarified by the author of the text.

amistre64 · Answer

does n=0,1,2,3,...  or n=1,2,3,4,...

anonymous · Answer

maybe you must represent the n by consecutively putting 1,2,3...,12 then add the sum.. am i correct?

amistre64 · Answer

that is an appropriate method yes, as long as that is the intent of the author that wrote your text

parthkohli · Answer

@amistre64 $n$th term is $3n - 2$. The first 12 terms are always a_1, a_2...a_12

harsimran_hs4 · Answer

yes you can always do that

amistre64 · Answer

0,1,2,3,...,11 is also a possible interpretation.

anonymous · Answer

are there some other way to answer this kind of situation?

parthkohli · Answer

Maybe. Well, you have $1,4,7,10\cdots$ which can be better done by the arithmetic series formula.

parthkohli · Answer

Or else you can always do @harsimran_hs4's method.

anonymous · Answer

ok sir tnx a lot

anonymous · Answer

is it 212 sir?

anonymous · Answer

i will close this already... thanks for all ur help. 1 more to go.

amistre64 · Answer

@parthkohli http://people.brandeis.edu/~igusa/Math23bS10/Math23b_S10_notes6.pdf the first 12 terms are not always a1,a2,a3, and are highly dependent on the author of the text. Notice their definition of a sequence. If n starts at 0, the 12th term is a11.

amistre64 · Answer

If the author of the text has chosen n=1,2,3,... for their particular definition, then that is what is to be used in the text.  If they have chosen n=0,1,2,3, .... then that is the rule to be followed for the text.

amistre64 · Answer

http://www.cs.sunysb.edu/~cse215/slides/seq_examples.pdf http://www.math.uvic.ca/faculty/gmacgill/guide/GenFuncs.pdf http://www.math.ust.hk/~mabfchen/Math232/Recurrence-Relation-Generating-Function.pdf and many more are examples of n=0,1,2,3,... and there are plenty of examples for the setup of n=1,2,3,4,....