First slide

Arithmetic progression

Question

The sum of 25 terms of an A.P., whose all the terms are natural numbers, lies between 1900 and 2000 and its 9^th term is 55. Then the first term of the A.P. is

Moderate

A

5
B

6
C

7
D

8

Solution

$\begin{array}{l} t_{9} = 55 \Rightarrow a + 8 d = 55 \\ S_{25} = \frac{25}{2} [2 a + 24 d] \\ = 25 (a + 12 d) \\ = 25 (55 + 4 d) \\ G. T 1900 < 25 (55 + 4 d) < 2000 \\ \Rightarrow 21 < 4 d < 25 \\ \Rightarrow d = 6 \\ \Rightarrow a = 7 \end{array}$

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