Question

The first sequence rule is add 4 starting from 15. The second sequence rule is add 3 starting from 18. What is the first number that appears in both sequences?

Answer 1

Answer: 27

Step-by-step explanation:

Given

In the first sequence, the first term is $a_1=15$

Common difference is $d_1=4$

In the second sequence, the first term is $b_1=18$

Common difference is $d_2=3$

The nth term of the sequence is $a_n=a+(n-1)d$

for the same number to appear on both sequence, the nth term must be equal

$\Rightarrow 15+(n-1)4=18+(n-1)3\\\Rightarrow 3=(n-1)\\\Rightarrow n=4$

Put n=4

$\Rightarrow 15+(4-1)4\\\Rightarrow 15+12=27$

Therefore, 27 is the first common term in both sequences.