Answer:
[tex]a_n=1+(n-1)4[/tex]
Step-by-step explanation:
Given : arithmetic series 1 + 5 + 9 + . . .
To Find: Which expression defines the arithmetic series 1 + 5 + 9 + . . . for seven terms?
Solution :
1 + 5 + 9 + . . .
a = first term = 1
d = common difference = 5-1=9-5=4
Formula of nth term = [tex]a_n=a+(n-1)d[/tex]
So, formula for nth term for given sequence [tex]a_n=1+(n-1)4[/tex]
So, [tex]a_n=1+(n-1)4[/tex] defines the arithmetic series 1 + 5 + 9 + . . . for seven terms
Now, formula of sum of n terms in A.P. = [tex]\frac{n}{2}(2a+(n-1)d)[/tex]
So, the sum of seven terms in given series = [tex]\frac{7}{2}(2\times1+(7-1)4)[/tex]
= [tex]\frac{7}{2}\times(26)[/tex]
= [tex]7\times13[/tex]
= [tex]91[/tex]
Thus the expression for the sum of seven terms = [tex]\frac{n}{2}(2a+(n-1)d)[/tex]
