Tim T. answered • 04/23/20

Math: K-12th grade to Advanced Calc, Ring Theory, Cryptography

Greetings! Lets solve this shall we ?

So, we must find the sum of this arithmetic sequence -1,2,5,8,11,14,17 using the arithmetic sequence formula and Sum of an Arithmetic Sequence formula such that

a_{n} = a_{1} + d(n-1)...........where a_{1} = -1 and a_{2} = 2. We can use this information to find the common sum ratio 'd' such that,

a_{2} = a_{1} + d(2-1)

2 = -1 + d(1)...........Then add 1 to both sides to get

3 = d

We do not need d to find the sum but i decided to show you how to find 'd' in case you needed to find the nth term.

The Sum Formula yields,

S_{n} = n(a_{1} + a_{7}) / 2, where n is the number if terms which is 7 in this case, right ? Then we plug in the first and seventh terms for a_{1} and a_{7} such that

**S**_{7}** = (7)(-1+17) / 2 = (7)(16/2) = (7)(8) = 56**

I hope this helped!