Question

In a new year , prince saved Rs 5oo in first week and then increased her weekly savings by 17.50. If in the ninth week , her weekly saving becomes Rs 207.50, find the value of n.​
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Answer 1

Answer:

$\huge \underbrace \mathfrak{ \red{a} \blue{n} \green{s} \pink{w} \purple{e} \pink{r}}$

✬ 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 ★

207.50 = 50 + (n – 1)17.50

207.50 = 50 + (17.50n – 17.50)

207.50 = 50 – 17.50 + 17.50n

207.50 = 32.5 + 17.50n

207.50 – 32.5/17.50 = n

175/17.50 = n

10 = n

Hence, value of n is 10.

Answer 2

Answer:$\huge\underbrace\mathcal\blue{anSwer}$

Weekly savings by prince in successive weeks are Rs.Rs. 50, Rs. 67.50 Rs. 85, Rs. 102.50.This is clearly an AP with a = 50, d = 17.50 and l = 207.50 <br> Let the number of terms of this AP be n. Then, <br>

=207.50=a+(n-1)d=207.50

=50+(n-1)×17.50=207.50

=(n-1)×17.50=207.50 - 50

(n-1)= 157.50

______.

17.50

=15750

_______ =9

1750

so n=10

Hence, prince's weekly savings will be Rs. 207.50 in 10th week.

✨✨hope it helps you dear

stay safe and blessed ✨✨