# 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.

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