What is the sum of a 16 term sequence where the last term is 21and the difference is -6?

Question

anonymous · Answer

@timo86m

anonymous · Answer

@lgbasallote ? This is different from my other question so I'm not understanding

lgbasallote · Answer

yeah...this takes more.. 

first you need to find the first term

lgbasallote · Answer

$$a_n = a_1 + (n-1)d$$
remember i said a_n is the last term? so in this case it would be 21
then common difference is -6
number of terms is 16

$$21 = a_1  + (16-1)(-6)$$
find a_1

anonymous · Answer

a1 is the 1st term so how am I supposed to find it?
Am I just suppose to simplify that? @lgbasallote

lgbasallote · Answer

yes. and then isolate a_1 just like in usual algebra

anonymous · Answer

I got 21= a1+ (-90)
 
What next?

lgbasallote · Answer

next you add 90 to both sides

anonymous · Answer

a1= 111?

lgbasallote · Answer

right. so now that's the first term.

now use $$S_n = \frac{n(a_n + a_1)}{2}$$
to get the sum

anonymous · Answer

What's Sn?

lgbasallote · Answer

sum of n terms

lgbasallote · Answer

that's what you're looking for

lgbasallote · Answer

just substitute n, a1 and an.. dont worry  about the notations

anonymous · Answer

I don't understand how to add a_21+111.

lgbasallote · Answer

a_21? where did that come from?

anonymous · Answer

the number of terms? I'm very confused can you solve the end so i can see what you did.

lgbasallote · Answer

$$\large \implies \frac{16(21 + 111)}{2}$$
remember what i said above
n = 16 <--because there are 16 terms
a_n =21 <--because it's the last term
a_1 = 111<--you solved for this

anonymous · Answer

Ohhhhh ok!

anonymous · Answer

I got 1056

anonymous · Answer

So 1,056 and 111 are both the answers?

lgbasallote · Answer

111 is not an answer...it's just looking for the sum..not the first term...so 1056 is the only answer`

anonymous · Answer

Thank youu

lgbasallote · Answer

welcome