Question

Find the sum S_n of the arithmetic sequence that satisfies the stated conditions

a_7=7/3, d=-2/3, n=15

Answer 1

a term in an arithmetic sequence is

\[a_{n} = a_{1} + (n -1) \times d\]

your goal is to find the 1st term in the sequence

\[a_{0}\]

knowing n = 7, and the d = -2/3 and a7 = 7/3

then when you find the 1st term you'll need


the formula for a the sum of an arithmetic sequence is

\[S_{n} = \frac{n}{2}[ 2a_{1} + (n - 1) \times d]\]

Answer 2

k, I got up to this point, im confused of how to get a1 when only given a7 and no other terms, if I had a6 or a8 I could figure it out, but I dont so I dont know how to plug a7 into the formula

Answer 3

Using campbell's first formula replace the n's with 7.

Answer 4

also replace d with -2/3

Answer 5

k got that much, how do I put in a7 when the formula calls for a1? do I need to find a1 first? If so how do I go about that?

Answer 6

replace a7 with what it equals

Answer 7

then solve the equation for a1

Answer 8

so just put 7/3 in the formula for a1? Because I tried that and got the wrong answer. Or what do you mean?

Answer 9

no a7 is 7/3

Answer 10

so replace a7 with 7/3

Answer 11

something tells me you aren't understanding that all you have to do is solve for a_1

Answer 12

replace d with what it equals which is -2/3
replace a7 with what it equals which is 7/3