Find the 14th term of the geometric sequence 10,-20,40, ...

The sequence is multiplying by - 2, so

x = 10 * (-2) ^n

x = 10 * (-2) ^14

x = 10 * 16 384

x = 163 840

Obviously each term is multiplied by - 2

an=a1 times r^ (n-1)

a1=first term

r=common ratio

r=-2

a1=10

an=10 times (-2) ^ (n-1)

n=14=14th term

a14=10 times (-2) ^ (14-1)

a14=10 times (-2) ^13

a14=10 times - 8192

a14=-81920

it is - 81920