Find the sum of the first 9 terms of the sequence. Show all work for full credit. 2, -7, -16, -25, ...

Answer 1

Hi Annie,

This is a classic problem and can be easily solved with a handy formula! First, you need to identify the sequence as geometric or arithmetic. Arithmetic sequences are adding at each step, while geometric sequences are multiplying. This sequence is clearly adding -9 at each step, so it's arithmetic.

To solve, you just need this formula: =n(a1​+an​​)/2. n is the number of terms you're counting to (9 in your case), a1 is the first term of the sequence, and an is the 9th term (in your case). That gives us this equation: 9(2 +(-70))/2, or 9(-68)/2, = -306!