Question

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

Then find a13​

Answer 1

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

And the term a (13) = 98

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