Natasha has to determain the number of toothpicks in the 15th step, step one has four toothpicks step two has 12 toothpicks and step three has 24 toothpicks. She does not want to draw 15 pictures then count the toothpicks. Explain or show how she could do this.

Answer 1

tn = a1 + (n-1)d

t2 = 12 and t3 = 24 so d= 24-13=11

so we need to find a1

t2=a1 + (n-1)d
12 = a1 + (2-1)11
12 = a1 +11
1 = a1

then

t15 = 1 + (15-1)11
t15 = 1 + 154
t15 = 155

Answer 2

use the arithmetic sequence formula
a(n)=a(1)+(n-1)d
last=first+(number-1)difference
?=4+(15-1)20
?=284

im pretty sure lol