Theory of Intelligence
11TH•Mathematics•Sequences And Series•Question 1

Overview

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.

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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