Class 10 Math All topics Arithmetic Progressions

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

(a)

$n=10$

(b)

$n=12$

(c)

$n=16$

(d)

$n=20$

Correct answer: (a)

Solution: Given that

$a=5$

$d=1.75$

$a_{n}=20.75$

$a_{n}=a+(n−1)d$

$20.75=5+(n−1)1.75$

$15.75=(n−1)1.75$

$a=5$

$d=1.75$

$a_{n}=20.75$

$a_{n}=a+(n−1)d$

$20.75=5+(n−1)1.75$

$15.75=(n−1)1.75$

$(n−1)=1.7515.75 =1751575 =763 =9$

$∴n−1=9$

$∴n=10$

$∴n−1=9$

$∴n=10$

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