# Chapter 10 - Section 10.3 - Geoetric Sequences and Series - Exercise Set - Page 1074: 57

$2435$

#### Work Step by Step

We are given that the sequence $a_n$ is an arithmetic sequence and the sequence $b_n$ is a geometric sequence. Here, we have $r=-2$ and $d=-15$ The general formula to find the nth term of a Geometric sequence is given as: $a_{n}=a_1r^{n-1}$ Thus, $a_{10}=a_1r^{10-1} =(-5)(-2)^9 =2560$ The general formula to find the nth term of an arithmetic sequence is given as: $a_{n}=a_1+(n-1) d$ and $b_{10}=10+(10-1) (-15) =10-135=-125$ Now, $a_{10}+b_{10}=2560-125=2435$

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