Write the explicit formula for the nth term of the arithmetic sequence 14, 28, 42.56
then find a13

The explicit formula of the given AP is  a(n)  = 7 + 7 n

And the term  a (13)  = 98

Step-by-step explanation:

Here, the given sequence  is :  14, 28 , 42, 56 ,

First Term (a)  = 14

Second term = 28

Now, the Common difference (d) = Second term - First Term

                                                      = 28 - 14 = 14

Now, the formula for nth term in an AP is :      a(n) = a + (n-1)d

So, here, the nth term of the sequence is given as:

a(n)  = 14  + (n-1) 7  

          = 14 + 7 n - 7 =  7 + 7 n

or, a(n)  = 7 + 7 n (1)

or, The explicit formula of the given AP is  a(n)  = 7 + 7 n

Now, for evaluating a (13) put n = 13 in (1)

⇒ a(13)  = 7 +  7 (13) =  7 + 91  = 98

or, a (13)  = 98

yes

yes yes yes