Answer:
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
