Question

Question 20 Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the n th week, her week, her weekly savings become Rs 20.75, find n.

Class 10 - Math - Arithmetic Progressions Page 107

Answer 1

Ramkali saved in 1st week = 5 ₹
and increase per week = 1.75₹

We absorb here,
5 , 6.75 , 8.5 ,.........20.75 are in AP
where, a = 5 , d = 1.75 and Tn = 20.75

Tn = a + ( n -1)d
20.75 = 5 + (n -1)1.75
15.75 = 1.75(n -1)
9 = n -1
n = 10

Answer 2

General term or nth term of A.P

The general term or nth term of A.P is given by an = a + (n – 1)d,
 where a is the first term, d is the common difference and n is the number of term.
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Given :

a = 5
d = 1.75
an = 20.75
n = ?

an = a + (n − 1) d
⇒20.75 = 5 + (n – 1) × 1.75
⇒20.75 - 5 =  (n – 1) × 1.75
⇒15.75 = (n – 1) × 1.75

(n – 1) = 15.75/1.75 = 1575/175
n-1= 63/7 = 9
n – 1 = 9
n = 10

Hence, n is 10.

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Hope this will help you....