Question

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

Answer 1

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

Answer 2

Answer:

$a_n=9n+17$

Step-by-step 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:  $a_n=9n+17$