Which expression defines the arithmetic series 1 + 5 + 9 + . . for seven terms?

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 =

So, formula for nth term for given sequence  

So,    defines the arithmetic series 1 + 5 + 9 + . . . for seven terms

Now, formula of sum of n terms in A.P. =

So, the sum of seven terms in given series =  

                                                                      =  

                                                                      =  

                                                                      =  

Thus the expression for the sum of seven terms =

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

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step-by-step explanation: