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

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.