Find the sum of the arithmetic sequence. -1, 2, 5, 8, 11, 14, 17

Question

A. 56
B. 63
C. -7
D. 20

Answer 1

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 = a₁ + d(n-1)...........where a₁ = -1 and a₂ = 2. We can use this information to find the common sum ratio 'd' such that,

a₂ = a₁ + 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(a₁ + a₇) / 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 a₁ and a₇ such that

S₇ = (7)(-1+17) / 2 = (7)(16/2) = (7)(8) = 56

I hope this helped!