A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic sequence 26, 44, 62, 80, ... . Find the total distance that the projectile traveled in seven seconds.

Question

A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic sequence 26, 44, 62, 80, ... .  Find the total distance that the projectile traveled in seven seconds.

anonymous · Answer

I got an answer of 152 ft in the 7 seconds.. is that correct?

lgbasallote · Answer

so first term is 26
the common difference is 18

$$a_n = a_1 + (n-1)d$$
$$a_7 = 26 + (7 - 1)(18)$$
$$a_7 = 26 + 6 \times 18$$
$$a_7 = 26 + 108$$
\doesnt sound like 152 to me

lgbasallote · Answer

i think you did 7 x 18?

anonymous · Answer

yes i did beccause it said 7 seconds haha

lgbasallote · Answer

you have to do 7-1..it's a common mistake :)

lgbasallote · Answer

i remember because it's looking for the 7th term so there are 7 terms so n=7

asnaseer · Answer

hang on guys...

lgbasallote · Answer

huh?

anonymous · Answer

i cant find that formula in my notes :/

asnaseer · Answer

are you sure you are answering the right question here?
it says find the "total distance" - not the distance travelled in the 7th sec

lgbasallote · Answer

uhmm oops

anonymous · Answer

yes its the distance traveled

asnaseer · Answer

:)

lgbasallote · Answer

wait...i wasnt finished o.O

anonymous · Answer

Find the total distance that the projectile traveled in seven seconds.

asnaseer · Answer

so you need to use the formula for the sum of an arithmetic series

asnaseer · Answer

I'll let @lgbasallote show you how...

lgbasallote · Answer

i was just finding the a7 for
$$s_n = \frac{n(a_1 + a_7}{2}$$
:p

lgbasallote · Answer

hehe :D

lgbasallote · Answer

so what would  be the 7th term?

anonymous · Answer

umm is a1 the first term and a7 the last term?

lgbasallote · Answer

yep

anonymous · Answer

so, the last term of whats given? cuz what about the "..." that means there are more terms :/

anonymous · Answer

ok, im just really confused

lgbasallote · Answer

yes because there are 7 terms but it only showed 4 terms..so they put a dotdotdot

lgbasallote · Answer

the last term is what we solved for

lgbasallote · Answer

that a7 thingy that we solved..that's the last term

lgbasallote · Answer

then you just apply the formula for arithmetic sequence

lgbasallote · Answer

sum of arithmetic sequence*

perl · Answer

General formula 
an = a1 + (n-1)d

Here we have
an = 26 + (n-1)*18

perl · Answer

now we want sum of an 
Sum (an) = 26*n +(n-1)(n)/2*18

perl · Answer

sum an from n=1..7
26*7 + 6*7*18/2 =560

anonymous · Answer

... i dont understand that at allllllllll

lgbasallote · Answer

do you understand what i did to find the 7th term?

anonymous · Answer

Does 560 sound right?