Formula
ARITHMETIC
PROGRESSIONS
Q.19) Subba Rao started work in 1995 at an annual salary of Rs.5000 and received an increment of Rs.200 each year. In which year did his income reach Rs.7000 ?
Sol:
Year 1995
Annual salary Rs.5000
Rise in salary
Year 1996
Annual salary Rs.5200
+ Rs.200
Year 1997
Annual salary Rs.5400
+ Rs.200
…
Annual salary Rs.7000
Year ?
Amount of annual salaries forms an AP
a1
a2
a3
an
We need to find n when an = 7000
Exercise 5.2 19
Q.19) Subba Rao started work in 1995 at an annual salary of Rs.5000 and received an increment of Rs.200 each year. In which year did his income reach Rs.7000 ?
Sol:
∴
The salaries of each year after 1995 are
Let after nth year, his salary will be Rs. 7000
∴ an = a + (n – 1)d
∴
7000
=
5000
+ (n – 1)
200
∴
7000
–
5000
= (n – 1)
200
∴
2000
= (n – 1)
200
∴
2000
200
= (n – 1)
10
1
∴
10
= n – 1
∴
n
= 10 + 1
∴
n
= 11
Therefore, in 11th year, his salary will be Rs.7000.
The incomes that Subba Rao obtained in various years form an A.P with first term (a) = 5000 and common difference(d) = 200
Now an = 7000
5000,
5200,
5400, ……,
7000
We need to find n when an = 7000