Question

In a new year , Reenu saved Rs 50 in first week and then increased her weekly savings by 17.50. If in the nth week , her weekly saving becomes Rs 207.50, find the value of n.​

Answer 1

✬ Value of n = 10 ✬

Step-by-step explanation:

Given:

• Money save by Reenu in first week is Rs 50.
• Money keeps increasing by Rs 17.50 every next week.
• In nth week her weekly saving becomes Rs 207.50.

To Find:

• What is the value of n ?

Solution: We will solve it by using formula of general term of an AP.

Total money saved by her in every week

➟ For 1st week = Rs 50

➟ For 2nd = (50 + 17.50) = Rs 67.50

➟ For 3rd = (67.50 + 17.50) = Rs 85

➟ For 4th = (85 + 17.50) = Rs 102.50

It will keep going like this to nth week

Here we observed that given sequence is in AP. So let's write first term and common difference.

• a {first term} = 50

• d {common difference} = 17.50

also

• aⁿ = 207.50

As we know that

★ aⁿ = a + (n – 1)d ★

$\implies{\rm }$ 207.50 = 50 + (n – 1)17.50

$\implies{\rm }$ 207.50 = 50 + (17.50n – 17.50)

$\implies{\rm }$ 207.50 = 50 – 17.50 + 17.50n

$\implies{\rm }$ 207.50 = 32.5 + 17.50n

$\implies{\rm }$ 207.50 – 32.5/17.50 = n

$\implies{\rm }$ 175/17.50 = n

$\implies{\rm }$ 10 = n

Hence, value of n is 10.

Answer 2

Given :

• Reenu saved Rs 50 in first week and then increased her weekly savings by 17.50.

• If in the nth week , her weekly saving becomes Rs 207.50,

To Find :

• find the value of n.

Solution :

This is clearly an Ap with

a = 50

d = 17.50

l = 207.50

Let the number of terms af this AP be n.Then,

A + (n - 1)d = 207.50

Substitute all values :

50 + (n - 1 ) × 17.50 = 207.50

(n - 1) × 17.50 = 207.50 - 50

(n - 1) × 17.50 = 157.50

(n - 1) = 157.50/17.50

(n - 1) = 9

N = 9 + 1

N = 10

Hence , Reenu 's weekly saving wiil be Rs.207.50 in 10 th week.