Test Index

Sequence and Series

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Question : 60 of 86

Marks: +1, -0

A person received the salary for the 1 st Year is

₹ 5,00,000

per year and he received an increment of

₹ 15,000

per year then the sum of the salary he taken in 10 years

$₹ 56,75,000$
$₹ 72,75,000$
$₹ 63,75,000$
None of these

Solution:

Concept:

The salaries form an arithmetic progression (AP) with first term ₹5,00,000 and common difference ₹15,000. The sum of the first

n

terms of an AP is given by

S_n = \frac{n}{2}[2a + (n-1)d]

.

Explanation:

First year salary

a = 5,00,000

Annual increment

d = 15,000

Number of years

n = 10

Sum

S_{10} = \frac{10}{2}[2 \times 5,00,000 + (10-1) \times 15,000]

= 5[10,00,000 + 9 \times 15,000]

= 5[10,00,000 + 1,35,000]

= 5 \times 11,35,000 = 56,75,000

Answer:

₹ 56,75,000

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