Question

Is 200 any term of the sequence 3, 7, 11, 15,...?

Answer 1

The given sequence is 3 , 7 , 11 ,15

$a_2$ - $a_1$ = 7 - 3 = 4

$a_3$ - $a_2$ = 11 - 7 = 4

$a_4$ - $a_3$ = 15 - 11 = 4

As $a_{k+1}$ - $a_k$ is the same for k = 1 ,2 ,3 etc , the given sequence form an AP.

Here , a = 3 , d= 4

Let 200 be the n th term of the given sequence. then ,

$a_n$ = 200

a + (n - 1) d = 200

3 + (n - 1) 4 = 200

( n- 1) = ( $\frac{197}{4}$)

n = $\frac{197}{4}$ + 1

n = $\frac{201}{4}$

But n should be a postive integer . So , 200 is not any term of the given sequence.