Question

Write an explicit formula for an, the nth term of the sequence 26, 35, 44, ....

Answer 1

`a_n=9n+17`

Explanation:

From inspection we can see that the sequence is an arithmetic sequence since the common difference between terms is constant.

General form of an arithmetic sequence formula:
`a_n=a+(n-1)d`

(where a is the first term and d is the common difference).

To find the common difference subtract one term from the next:

`d = 44-35=9`

or
`d=35-26=9`

Given:

• 
  `a=26`
• 
  `d=9`

Therefore,
`a_n=26+(n-1)9`

Simplified:
`a_n=9n+17`

Answer 2

Here , we need to find an formula for nth term of the sequence 26 , 35 , 44 , .....

Now , here if you notice carefully ,then you can notice that 35 - 26 = 9 , 44 - 35 = 9 , So the given sequence is an AP ( Arithmetic Progression ) with common difference being 9 , first term being 26 , so now as we knows that :

• 
  `{\boxed{\bf{a_(n)=a+(n-1)d}}}`

Where ,
`{\bf{a_n}}` is nth term of AP ,
`\bf a` being first term while
`\bf d` is the common difference . So , now putting the values in above formula ;

`{:\implies \quad \sf a_(n)=26+(n-1)9}`

`{:\implies \quad \sf a_(n)=26+9n-9}`

`{:\implies \quad \bf \therefore \quad \underline{\underline{a_(n)=9n+17}}}`

Henceforth , nth term of the sequence is 9n+17