Question

If a pattern consists of n shapes formed by line segments of equal lengths and the number of line segments required to make n shapes is given by the algebraic expression:

• A. $2n+1$
• B. $3n+1$
• C. $3n+2$
• D. 5n+1
• E. 5n+2
• F. 4n+3

Answer 1

The correct option is A $2n+1$

i) 2n+1

Taking n=5,10,100,we get

$2\times 5+1=11$

$2\times 10+1=21$

$2\times 100+1-201$

ii) $3n+1$

Taking n=5,10,100,then we get

$3\times 5+1=16$

$3\times 10+1=31$

$3\times 100+1=301$

iii) $3n+2$

Taking n=5,10,100,then we get

$3\times 5+2=17$

$3\times 10+2=32$

$3\times 100+2=302$

iv) $5n+1$

Taking n=5,10,100,then we get

$5\times 5+1=26$

$5\times 10+1=51$

$5\times 100+1=501$

v) $5n+2$

Taking $n=5,10,100,$then we get

$5\times 5+2=27$

$5\times 10+2=52$

$5\times 100+2=502$

vi) $4n+3$

Taking n=5,10,100,then we get

$4\times 5+3=23$

$5\times 10+3=53$

$5\times 100+3=503$