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Home » A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. (a) Find his salary for the tenth month (b) What is his total earnings during the first year?
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. (a) Find his salary for the tenth month (b) What is his total earnings during the first year?
CBSE | Class 11 | Maths | NCERT Exemplar | Sequences and Series
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. (a) Find his salary for the tenth month (b) What is his total earnings during the first year?

Solution:

It is given to us that in first month the man’s salary is Rs.5200 and then it increases by Rs.320 every month

Therefore, 5200, 5200 + 320, 5200 + 640… will be the sequence so formed of his salary per month.

Here the common difference is d = 320

a) We now have to find the 10thterm of the AP that is salary in 10thmonth

nth term of AP is denoted by tn =\text{ }a\text{ }+\text{ }\left( n\text{ }\text{-}1 \right)\text{ }d

Where the first term is ‘a’ and the common difference is ‘d’

We need to find t10

\Rightarrow ~{{t}_{10}}~=\text{ }5200\text{ }+\text{ }\left( 10{-}1 \right)\text{ }\left( 320 \right)

\Rightarrow ~{{t}_{10}}~=\text{ }5200\text{ }+\text{ }2880

\Rightarrow ~{{t}_{10}}~=\text{ }8080

As a result the salary in 10th month is Rs.8080

b) In order to get the total earnings in first year we need to add the first 12 terms of the sequence so obtained i.e. we need to find S12

Sum of first n terms of the AP formed is given by {{S}_{n~}}=\text{ }n/2\text{ }\left( 2a\text{ }+\text{ }\left( n {-}1 \right)\text{ }d \right)

Where the first term is ‘a’ and the common difference is ‘d’

{{S}_{12}}~=\text{ }\left( 12/2 \right)\text{ }\left( 2\text{ }\left( 5200 \right)\text{ }+\text{ }\left( 12{-}1 \right)\text{ }320 \right)

\Rightarrow ~{{S}_{12}}~=\text{ }6\left( 10400\text{ }+\text{ }11\left( 320 \right) \right)

\Rightarrow ~{{S}_{12}}~=\text{ }6\left( 10400\text{ }+\text{ }3520 \right)

\Rightarrow ~{{S}_{12}}~=\text{ }6\left( 13920 \right)

\Rightarrow ~{{S}_{12}}~=\text{ }83520

Therefore, Rs.83520 is his total earnings in first year.

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