Question

Is 2000 a term of this sequence 108,117,126,135​

Answer 1

Answer:

No

Step-by-step explanation

Acooding to the equation f+(n-1)d,n is not satisfied by 2000

Answer 2

Answer:

2000 is not a term of the sequence 108,117,126,135​..............

Step-by-step explanation:

Given sequence is 108,117,126,135,.........

Required to find whether 2000 is a term of this sequence

Recall the concept

The nth term of an AP is given by  $a_n$ = a+(n-1)d, where 'a' is the first term and 'd' is the common difference of the AP.

Solution

Given sequence is 108,117,126,135,.........

The given sequence form an AP, since 117 -108 = 126 -117 = 9

Here, the first term of this AP = a = 108

Common difference = d = 9

To check 2000  is a term of sequence 108,117,126,135​....,

we need to check whether 2000 = $a_{n}$, for some natural number  'n'

If  $a_{n}$ = 2000

a + (n-1)d = 2000

Substituting the value of 'a' and 'd' in the above equation

108 + (n-1)9 = 2000

9(n-1) = 2000 - 108 = $\frac{1892}{9}$

n-1 = 210.22

n = 210.222+1

= 211.222, which is not a natural number

Hence, there is no term  $a_{n}$ = 2000 for any natural number 'n'

∴ 2000 is not a term of the sequence 108,117,126,135​..............

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