Question

The diagram below represents the first three terms of a sequence. Assuming the pattern continues,which formula determines an, the number of squares in the nth term ?

Answer 1

We will count number of squares

first term is 4

so, $a_1=4$

second term is 7

so, $a_2=7$

third term is 10

so, $a_3=10$

We can see that this sequence is in arithematic sequence

we can use nth term formula

$a_n=a_1+(n-1)d$

where

an is nth terms

a1 is first term

d is common difference

n is total number of terms

$d=7-4=3$

now, we can plug values

and we get

$a_n=4+(n-1)*3$

$a_n=4+3n-3$

$a_n=1+3n$

$a_n=3n+1$.................Answer