The first four terms of a geometric sequence are 7, 14, 28, and 56. Find the 20th term.

Answer 1

each term is twice the preceding term

a2 = a1(r^n-1)

a20 = 7(2^19) = seven times two times two times two .... (19 tines)

= 3,670,016

a1 = 7

a2 = 14

a3 = 28

a4 = 56

a5 = 112

a6 = 224

a7 = 448

a8 = 896

a9 = 1792

a10 = 3584

a11 = 7168

a12 = 14,336

a13 = 28,672

a14 = 57,344

a15= 114,688

a16 = 229,376

a17 = 458,752

a18 = 917,504

a19 = 1,835,008

a20 = 3,670,016

Answer 2

nth term of geometric sequence:

an = a1 * r ^ n-1

to find r, divide 2nd number by 1st number = 14/7 = 2

a1 is 7

substituting

a20 = 7 * 2^19 = 3,670,016