Question

In the arithmetic sequence 10,16,22 Is 280 a term of this sequence

Answer 1

Step-by-step explanation:

Given :-

The Arithmetic Sequence 10,16,22,...

To find:-

Is 280 a term in the given AP?

Solution:-

Given AP : 10,16,22,...

First term (a) = 10

Common difference (d) = 16-10 = 6

We know that

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

Let an = 280

=> a+(n-1)d = 280

On Substituting the values of a and d in the above formula then

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

=> 10+6n-6 = 280

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

=> 4+6n = 280

=> 6n = 280-4

=> 6n = 276

=> n = 276/6

=>n = 46

The value of n = 46

46th term = 280

Answer:-

280 belongs to the given AP and it is the 46th term of the given AP.

Check :-

46th term = a46

=> a+(46-1)d

=> a+45d

=> 10+45(6)

=> 10+270

=> 280

Verified the given relations in the given problem

Used formulae:-

• The general term of an AP

= an = a+(n-1)d

• a = First term

• d = Common difference

• n = Number of terms