#MAASL00261

a) Recognize the pattern of line segments:

Sequence: 7, 13...

Find the common difference in the arithmetic sequence

u_{2}-u_{1}=13-7=6

d=6

Derive arithmetic sequence formula

u_{n}=u_{1}+(n-1)d

u_{n}=7+(n-1)6

Set equal to 325 and solve for n

325=7+(n-1)6

318=(n-1)6

53=n-1

n=54

X=54



b) Sum of arithmetic sequence formula: 

S_{n}=\frac{n}{2}[2u_{1}+(n-1)(d)]

S_{23}=\frac{23}{2}[2(7)+(23-1)(6)]

S_{23}=\frac{23}{2}[146]

S_{23}=1679

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