Theory of Intelligence
11TH•Mathematics•Sequences And Series•Exercise 6.11

6.11 Real Life Problems involving Sequences and Series

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Question 1

A sum of Rs.10400 is paid off in 40 instalments such that each instalment is Rs.10 more than the preceding instalment. Calculate the value of the first instalment.

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Step-by-Step Solution

Question 1

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Let the first instalment be ( a ) rupees.
Common difference ( d = 10 ).
Number of instalments ( n = 40 ).
Total sum ( S_{40} = 10400 ).

[ S_{40} = \frac{40}{2}\bigl[2a + (40-1)\cdot 10\bigr] = 20\bigl[2a + 390\bigr] = 40a + 7800. ]

[ 40a + 7800 = 10400 \implies 40a = 2600 \implies a = 65. ]

Answer: Rs. 65

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