# Sequence Within A Sequence 5

**Algebra**Level 4

Consider a sequence of numbers \(T_1, T_2, T_3, \ldots, T_n\) (\(n\in \mathbb{Z}^+\)) that satisfies the following: \[T_1=5, d_1=1\] \[T_2=T_1+d_1 \\ T_3=T_2+d_2 \\ \vdots \\ T_n=T_{n-1}+d_{n-1}\] \[d_k=2d_{k-1},~~~k=2, 3, 4, \ldots, n-1\]

Denote \(S_a=T_1+T_2+\ldots+T_a\), find \(S_{16}\).

<<Sequence Within A Sequence 4

This is one part of 1+1 is not = to 3.