Question

To replace the trees destroyed by typhoon Yolanda, the forestry department of Tagaytay has developed a ten-year plan. During the first year they will plant 100 trees. Each succeeding year, they will plant 50 more trees than they planted the year before.

Answer 1

a. 1,000 trees

b. 3,250 trees

Explanation:

a. How many trees will they plant during the fifth year?

b. How many trees will they have planted by the end of the tenth year?​

Using the sum of an arithmetic progression formula

Sn = n/2 {2a+(n-1)d}

Where,

Sn = Sum of an n terms

n = number of terms

a = first term

d = common difference

a.

n = 5

a = 100

d = 50

S5 = n/2 {2a+(n-1)d}

= 5/2 {2*100 + (5-1)50}

= 5/2 {200+(4)50}

= 5/2{200 + 200}

= 5/2(400)

= 2,000 / 2

= 1,000

S5 = 1,000 trees

b. Sn = n/2 {2a+(n-1)d}

n = 10

a = 100

d =50

S10 = 10/2{2*100 + (10-1)50}

= 5{200 + (9)50}

= 5{200 + 450}

= 5(650)

= 3,250

S10 = 3,250 trees