Question

A grandparent gives a grandchild £100 at birth, and promises to increase the gift by £5 on each subsequent birthday.

a. Show that the grandchild will receive £200 on the 20𝑡ℎ birthday.

b. If the child has saved all the money, what is the total amount at age 20?

c. By how much would the gift have to increase each year if the total at age 20 is to be £4,200?

Answer 1

d=5

a1= £100

a₂= £105 one year old

a₃= £110 two years old

.....

a₂₁ =? twenty yearIs old

a.)

Arithmetic progression formula:

a_n = a₁ + d * (n-1)

a₂₁ = 100 + 5 * 20 = 200

b.)

arithmetic progression The formula for finding the sum of n terms:

$S_n=\cfrac{n} {2}* (2a+(n-1)d)$

$S_{21}= \cfrac {21}{2}*(2*100+(21-1)*5)= \bold{3150}$

c.)

$S_n=\cfrac{n} {2}* (2a+(n-1)d)$

$4200=\cfrac{21} {2}* (2*100+(21-1)d)$

4200 = 2100 + 210d

210d = 2100

d= 10