Respuesta :
The expression defines the given series for seven terms, i don't understand the question but i do know the sum which you should know to
15 + 19 + 23 = 57
Sorry
15 + 19 + 23 = 57
Sorry
Answer:
The expression is [tex]\sum _{n=1}^7\:\left(11+4n\right)[/tex] and sum of first seven terms is 189.
Step-by-step explanation:
Given : The series 15 + 19 + 23 + . . .
We have to find an expression that defines the series for seven terms .
15 can be written as 11 + 4(1)
19 can be written as 11 + 4(2)
23 can be written as 11 + 4(3)
and so on
Thus, in general for 7 terms,
We can write it as [tex]\sum _{n=1}^7\:\left(11+4n\right)[/tex]
Thus, [tex]\sum _{n=1}^7\:\left(11+4n\right)[/tex]
Apply the sum rule, [tex]\sum a_n+b_n=\sum a_n+\sum b_n[/tex]
[tex]=\sum _{n=1}^711+\sum _{n=1}^74n[/tex]
Consider, [tex]\sum _{n=1}^711[/tex],
[tex]\mathrm{Apply\:the\:Sum\:Formula:\quad }\sum _{k=1}^n\:a\:=\:a\cdot n[/tex]
[tex]\sum _{n=1}^711=77[/tex]
Now, Consider [tex]\sum _{n=1}^74n[/tex]
[tex]\mathrm{Apply\:the\:constant\:multiplication\:rule}:\quad \sum c\cdot a_n=c\cdot \sum a_n[/tex]
[tex]=4\cdot \sum \:_{n=1}^7n[/tex]
[tex]\sum _{n=1}^74n=112[/tex]
Thus, [tex]\sum _{n=1}^711+4n=189[/tex]
Thus, the expression is [tex]\sum _{n=1}^7\:\left(11+4n\right)[/tex] and sum of first seven terms is 189.
