Sum of this sequence: a_1 = 10, a = 3 + a_{n-1}

unknownren

New member
Joined
Feb 17, 2019
Messages
3
Explain is it possible to find the sum of the sequence in this problem.
 

Attachments

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,134
Explain is it possible to find the sum of the sequence in this problem.

Your expression needs to be corrected! You posted:

a1 = 10

\(\displaystyle a_{[?]} \ = \ a_{n-1} + 3\)

On the left-hand-side of the equation there is no refernce to an!
 

unknownren

New member
Joined
Feb 17, 2019
Messages
3
Your expression needs to be corrected! You posted:

a1 = 10

\(\displaystyle a_{[?]} \ = \ a_{n-1} + 3\)

On the left-hand-side of the equation there is no refernce to an!

Thanks for your response!

So its not possible to find the sum of this sequence then? an! is added to the left hand side correct?


 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,784
Thanks for your response!

So its not possible to find the sum of this sequence then? an! is added to the left hand side correct?


To SUM a sequence, it must either END or CONVERGE (in some appropriate sense).

Adding three to each successive term does neither.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,039
Explain is it possible to find the sum of the sequence in this problem.
Presumably you are asking about finding the sum of the first N terms in the sequence defined by

a1 = 10
an = an-1 + 3

Write out the first several terms of this sequence, and the corresponding sums, in order to get a sense of what you are working with.

Then look up "arithmetic series", and see if you can apply what you learn. Show us whatever you are able to do, and we'll help you out.
 

unknownren

New member
Joined
Feb 17, 2019
Messages
3
Presumably you are asking about finding the sum of the first N terms in the sequence defined by
a1 = 10
an = an-1 + 3

Write out the first several terms of this sequence, and the corresponding sums, in order to get a sense of what you are working with.

Then look up "arithmetic series", and see if you can apply what you learn. Show us whatever you are able to do, and we'll help you out.
a2=3+10=13
a3=3+13=16
a4=3+16=19
a5=3+19=22

a2-a1=13-10=3
a3-a2=16-13=3
a4-a3=19-16=3
a5-a4=22-19=3

common difference is 3
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,134
a2=3+10=13
a3=3+13=16
a4=3+16=19
a5=3+19=22

a2-a1=13-10=3
a3-a2=16-13=3
a4-a3=19-16=3
a5-a4=22-19=3

common difference is 3
Do you know the sum of first 'n' terms in an arithmatic series with first term 'a' and common difference 'd'?
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,039
a2=3+10=13
a3=3+13=16
a4=3+16=19
a5=3+19=22

a2-a1=13-10=3
a3-a2=16-13=3
a4-a3=19-16=3
a5-a4=22-19=3

common difference is 3
Good; you saw where I was leading you. (Did you notice that the definition itself tells you the common difference: an - an-1 = 3 .)

What more do you know about arithmetic series?
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,813
Explain is it possible to find the sum of the sequence in this problem.
Not being sure of what really what the question is, I take Prof. Peterson's reading.
If \(\displaystyle a_1=10~\&~a_{n}=a_{n-1}+3\) then \(\displaystyle a_n=3n+7\) SEE HERE
\(\displaystyle \begin{align*}S_n&=\sum\limits_{k = 1}^n {{a_k}}\\&=\sum\limits_{k = 1}^n {3k+7}\\&=3\dfrac{n(n+1)}{2}+7n\\&=~? \\ \end{align*}\)


 
Top