Question

Is 280 is term of the sequence 10, 16, 22, … ? Why ?

Answer 1

Step-by-step explanation:

Given :-

10,16,22,...

To find :-

Is 280 is term of the sequence 10, 16, 22, … ? Why ?

Solution :-

Given that

10,16,22,...

First term = 10

Second term = 16

Common difference = 16-10 = 6

and

22-16 = 6

The common difference is same throughout the series so they are km the AP

So Given sequence is an AP

Now,

We have,

First term (a) = 10

Common difference (d) = 6

Let nth term of the AP = 280

We know that

nth term of an AP = an = a+(n-1)d

Let an = 280

On substituting these values in the above formula

=> 10+(n-1)(6) = 280

=> 10+6n-6 = 280

=> 6n +4 = 280

=> 6n = 280-4

=> 6n = 276

=> n = 276/6

=> n = 46

The value of n is the natural number.

It exists .

The number of terms = 46

So, 280 is the 46th term of the AP.

Answer:-

280 is in the given sequence ,it is 46th term of the sequence.

Used formulae:-

→ nth term of an AP = an = a+(n-1)d

• a = First term
• d = Common difference
• n = Number of terms
• an = nth or general or last term