● Let us consider the situation again, given in Section 5.1 in which Reena applied for a job and got selected. She has been offered the job with a starting monthly salary of Rs. 8000, with an annual increment of Rs. 500. What would be her monthly salary for the fifth year?
● To answer this, let us first see what her monthly salary for the second year would be.
● It would be Rs. (8000 + 500) = Rs. 8500. In the same way, we can find the monthly salary for the `3rd, 4th` and `5th` year by adding Rs. 500 to the salary of the previous year. So, the salary for the 3rd year = Rs. (8500 + 500)
`= Rs. (8000 + 500 + 500)`
`= Rs. (8000 + 2 × 500)`
`= Rs. [8000 + (3 – 1) × 500]` (for the 3rd year)
`= Rs. 9000`
Salary for the 4th year `= Rs. (9000 + 500)`
`= Rs. (8000 + 500 + 500 + 500)`
`= Rs. (8000 + 3 × 500)`
`= Rs. [8000 + (4 – 1) × 500]` (for the 4th year)
`= Rs. 9500`
Salary for the 5th year = Rs. (9500 + 500 )
`= Rs. (8000+500+500+500 + 500)`
`= Rs. (8000 + 4 × 500)`
`= Rs. [8000 + (5 – 1) × 500]` (for the 5th year)
`= Rs. 10000`
Observe that we are getting a list of numbers `8000, 8500, 9000, 9500, 10000, . . .`
● These numbers are in AP.
● Now, looking at the pattern formed above, can you find her monthly salary for the 6th year? The 15th year? And, assuming that she will still be working in the job, what about the monthly salary for the 25th year?
You would calculate this by adding Rs. 500 each time to the salary of the previous year to give the answer. Can we make this process shorter?
Let us see. You may have already got some idea from the way we have obtained the salaries above.
Salary for the 15th year
= Salary for the 14th year + Rs. 500
● Let us consider the situation again, given in Section 5.1 in which Reena applied for a job and got selected. She has been offered the job with a starting monthly salary of Rs. 8000, with an annual increment of Rs. 500. What would be her monthly salary for the fifth year?
● To answer this, let us first see what her monthly salary for the second year would be.
● It would be Rs. (8000 + 500) = Rs. 8500. In the same way, we can find the monthly salary for the `3rd, 4th` and `5th` year by adding Rs. 500 to the salary of the previous year. So, the salary for the 3rd year = Rs. (8500 + 500)
`= Rs. (8000 + 500 + 500)`
`= Rs. (8000 + 2 × 500)`
`= Rs. [8000 + (3 – 1) × 500]` (for the 3rd year)
`= Rs. 9000`
Salary for the 4th year `= Rs. (9000 + 500)`
`= Rs. (8000 + 500 + 500 + 500)`
`= Rs. (8000 + 3 × 500)`
`= Rs. [8000 + (4 – 1) × 500]` (for the 4th year)
`= Rs. 9500`
Salary for the 5th year = Rs. (9500 + 500 )
`= Rs. (8000+500+500+500 + 500)`
`= Rs. (8000 + 4 × 500)`
`= Rs. [8000 + (5 – 1) × 500]` (for the 5th year)
`= Rs. 10000`
Observe that we are getting a list of numbers `8000, 8500, 9000, 9500, 10000, . . .`
● These numbers are in AP.
● Now, looking at the pattern formed above, can you find her monthly salary for the 6th year? The 15th year? And, assuming that she will still be working in the job, what about the monthly salary for the 25th year?
You would calculate this by adding Rs. 500 each time to the salary of the previous year to give the answer. Can we make this process shorter?
Let us see. You may have already got some idea from the way we have obtained the salaries above.
Salary for the 15th year
= Salary for the 14th year + Rs. 500