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

Answer:The explicit formula of the given AP is  a(n)  = 7 + 7 nAnd the term  a (13)  = 98Step-by-step explanation:Here, the given sequence  is :  14, 28 , 42, 56 ,....First Term (a)  = 14Second term = 28Now, the Common difference (d) = Second term - First Term                                                       = 28 - 14 = 14Now, the formula for nth term in an AP is :      a(n) = a + (n-1)dSo, here, the nth term of the sequence is given as:a(n)  = 14  + (n-1) 7             = 14 + 7 n - 7 =  7 + 7 nor, a(n)  = 7 + 7 n ......... (1)or, The explicit formula of the given AP is  a(n)  = 7 + 7 nNow, for evaluating a (13) put n = 13 in (1)⇒ a(13)  = 7 +  7 (13) =  7 + 91  = 98or, a (13)  = 98