MATH SOLVE

2 months ago

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

Accepted Solution

A:

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