Kevin and anita are writing poems. kevin has no poems to start, and writes three new poems each day. anita has four poems to start, and writes two new poems each day. after how many days will they have the same number of poems in their collections? (a) 1 day(b) 2 days(c) 3 days(d) 4 days

Given kevin has no poems to start, and writes three new poems each day While

Anita has four poems to start, and writes two new poems each day.

Total number of poems on Day 1 by Kevin =3

Total number of poems on day 1 by Anita = 4+2=6

Total number of poems on Day 2 by Kevin =3+3=6

Total number of poems on Day 2 by Anita =6+2=8

Total number of poems on Day 3 by Kevin 6+3=9

Total number of poems on Day 3 by Anita =8+2=10

Total number of poems on Day 4 by Kevin=9+3=12

Total number of poems on Day 4 by Anita =10+2=12

On day 4 they will have same number of poems .

Option (D) 4 days is the right answer.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for