Question

Write an explicit formula for the arithmetic sequence below and use it to find the 52nd term:

25, 19, 13, 7

Answer 1

The explicit term is 31-6n

the 52nd term is -281

Explanation:

Mathematically, the nth term of an arithmetic sequence is;

Tn = a + (n-1)d

a is first term = 25

d is common difference = 19-25 = 13-19 = 7-13 = -6

So for the explicit formula;

Tn = 25 + (n-1) -6

Tn = 25 -6n + 6 = 31-6n

for the 52nd term;

T52 = 25 + (52-1)-6

= 25 -306 = -281