Find the missing term in this geometric sequence:

2, (?),98

The missing term is 14

Step-by-step explanation:

The sequence is a geometric sequence. The first term is 2 and the third term is 98. The question wants us to find the second term.

Since we know the 3rd term the common ratio can be solved using the nth term equation for geometric sequence

nth term = arⁿ⁻¹

where

r = common ratio

n = number of terms

nth term = arⁿ⁻¹

98 = 2r³⁻¹

98 = 2r²

divide both sides by 2

r² = 98/2

r² = 49

square root both sides

r = √49

r = 7

The common ratio is known let us find the second term which is the missing term.

nth term = arⁿ⁻¹

arⁿ⁻¹

2 * 7²⁻¹

2 * 7 = 14

The missing term is 14