Question

a tree branch has 5 bonds. each day 2 more buds sprout. How many buds are on the tree brach after the first 5 days?

Answer 1

A tree branch has 5 bonds and each day 2 more buds sprout. Then

• after first day the tree will have 5+2=7 bonds;
• after second day the tree will have 7+2=9 bonds;
• after third day the tree will have 9+2=11 bonds;
• after fourth day the tree will have 11+2=13 bonds;
• after fifth day the tree will have 13+2=15 bonds.

Answer: 15 bonds.

Mathematically, this is an arithmetic sequence with
`a_1=5` and
`d=2.`

Th n-th term can be found using formula

`a_n=a_1+(n-1)d.`

Then

`a_6=5+(6-1)2=5+5\cdot 2=5+10=15.`

Here you have to find
`a_6`, because after 1st day you get
`a_2` and so on, after 5th day you get
`a_6`