Question

I need someone to check my work!! What is the sum of the arithmetic sequence 9, 14, 19, …, if there are 36 terms?
answer: 3,474
What is the sum of the arithmetic sequence 308, 304, 300, …, if there are 23 terms?
answer: 6,072

Answer 1

For the first one, the difference between terms is 5 and there are 35 steps.
9 + 35(5) = ?
For the second, the sequence decreases with each step. So answer must be less than 308, right?

Answer 2

for the second one
\[a_{23} = 308 + (23 - 1)(-4)\]
\[\implies 308 -88\]
\[\implies220\]
\[s_n = \frac{23(308 + 220)}{2}\]
\[s_n = 6,072\]

Answer 3

okay ty.

Answer 4

for the first one
\[a_{36} = 9 + (36-1)(5)\]
\[\implies 9 + 175\]
\[\implies 184\]
\[s_n = \frac{36(184 + 9)}{2}\]
\[\implies 3,474\]

Answer 5

ty :)