Question

the first negative term of the sequence 65,62 ,59 is​

Answer 1

SOLUTION

TO DETERMINE

The first negative term of the sequence 65 , 62 , 59 ,..

EVALUATION

Here the given sequence is 65 , 62 , 59 ,..

It is an arithmetic progression

First term = a = 65

Common Difference = d = 62 - 65 = - 3

Let nth term is the first negative term of the sequence

So by the given condition

$\sf \: a_n < 0$

$\sf \implies \: a + (n - 1)d < 0$

$\sf \implies \: 65 - 3 (n - 1) < 0$

$\sf \implies \: 3(n - 1) > 65$

$\sf \implies \: 3n - 3 > 65$

$\sf \implies \: 3n > 68$

$\sf \implies \: n > \dfrac{68}{3}$

Hence the smallest value of n satisfying the above condition is n = 23

The value of term

= a + 22d

= 65 - 66

= - 1

Hence 23rd term of the sequence is the first negative term of the sequence and it is - 1

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