Question

A girl walking uphill covers a distance of 20m during the first minute,18m during the second minute and 16m during third minute and so on . How much distance will she cover in i) 10th minute ii)10minutes

Answer 1

Answer:

i) 10th minute = 2 meter

ii)10 minutes = 110 meters

Step-by-step explanation:

Since she is less covering distance every minute i.e. 20, 18, 16,...

The given sequence is Arithmetic Progression.

Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.

i)- For finding the nth term, we use formula

aₙ = a + (n - 1) d

where, aₙ = value of nth term

a = First term

n = number of term

d = difference

Now, In given sequence: 20, 18, 16,...

a = 20, d = -2, n = 10

∴ aₙ = 20 + (10 - 1) × (-2)

⇒ aₙ = 20 - 18 = 2

Thus at 10th minute she will cover only 2m distance.

ii)- Now For calculating the total distance cover till 10 minute is equal to sum of all which can be calculate by formula:

$S_{n}= \frac{n}{2}[2a + (n-1)d]$

⇒ Sₙ = 5 × [ 2 × 20 + (10 - 1) × (-2)]

⇒ Sₙ = 5 × [ 40 - 18] = 110

Thus, She will cover total 110 meter of distance.

Answer 2

Step-by-step explanation:

20 , 18 , 16................ so on...

so a= 20