Question

Ramkall saved Rs. 5 In the first week of a year and then Increased her weekly savings by Rs. 1.75. If in the n^th week. her weekly savings become Rs. 20.75. find ‘n’.

Answer 1

Savings in the First week = Rs. 5. 

Savings in the Second week 5 + 1.75 = Rs. 6.75 

Savings in ‘n^th week is Rs. 20.75 

∴ A.P. 5, 6, 75 , …………. , 20.75 

a = 5, d = 6.75 – 5 = 1.75, a_n = 20.75. 

n =? 

a + (n – 1) d = a_n 

5 + (n – 1) (1.75) = 20.75 

5 + 1.75n – 1.75 = 20.75 

1 .75n + 3.25 = 20.75 

1.75n = 20.75 – 3.25 

1.75n = 17.5

∴ n = \(\frac{17.5}{1.75}\)

∴ n = \(\frac{1750}{175}\)

∴ n = 10 

∴ In the 10th week her savings becomes Rs. 20.75.