Determine the 10th term of the sequence 3,10,28,72,176. state the general term

Answer 1

n = 1

a1 = 3 = 1 * 3 = 1 * ( 2 * 1 + 1 ) = 2 ^ 0 ( 2 n + 1 ) = 2 ^ ( n - 1 ) ( 2 n + 1 )

n = 2

a2 = 10 = 2 * 5 = 2 * ( 2 * 2 + 1 ) = 2 ^ 1 ( 2 n + 1 ) = 2 ^ ( n - 1 ) ( 2 n + 1 )

n = 3

a3 = 28 = 4 * 7 = 4 * ( 2 * 3 + 1 ) = 2 ^ 2 ( 2 n + 1 ) = 2 ^ ( n - 1 ) ( 2 n + 1 )

n = 4

a4 = 72 = 8 * 9 = 8 * ( 2 * 4 + 1 ) = 2 ^ 3 ( 2 n + 1 ) = 2 ^ ( n - 1 ) ( 2 n + 1 )

n = 5

a5 = 176 = 16 * 11 = 16 * ( 2 * 5 + 1 ) = 2 ^ 4 ( 2 n + 1 ) = 2 ^ ( n - 1 ) ( 2 n + 1 )

SO :

an = 2 ^ ( n - 1 ) ( 2 n + 1 )

a10 = 2 ^ ( 10 - 1 ) * ( 2 * 10 + 1 ) =

2 ^ 9 * ( 20 + 1 ) = 512 * 21 = 10752