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.

A) 534
B) 560
C) 212
D) 426

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.

A) 534
B) 560
C) 212
D) 426

anonymous · Answer

DON'T JUST CHOOSE SOME ANSWER EXPLAIN IT!

anonymous · Answer

@campbell_st try this please

parthkohli · Answer

$\Large \color{purple}{\rightarrow a_{n} = a_{1} + (n - 1)d }$

parthkohli · Answer

Common difference is d(18)
a1 is the first term: 26

parthkohli · Answer

You have to find a7

campbell_st · Answer

ok... you know the 1st term a = 26 and you are asked to find the sum of the 1st 7 terms 

this needs the formula

$$s _{n} = \frac{n}{2} [2a + (n-1)d]$$

the common difference is $$T _{2} - T _{1} =$$
check its the same as $$T _{3}-T _{2}=$$

then n = 7, a = 26 and your d value substitute and evaluate

parthkohli · Answer

$\Large \color{purple}{\rightarrow a_{7} = 26 + 18(7 - 1) }$

parthkohli · Answer

So, a7 = 26 + 18(6)
a7 = 26 + 108
a7 = 134

parthkohli · Answer

Got it?

parthkohli · Answer

The common difference in an arithmetic sequence is:

$\Large \color{purple}{\rightarrow a_{n+ 1} - a_{n} }$

anonymous · Answer

134 isnt any of those answers and those r the only answers they give me on my optional study guide

parthkohli · Answer

Oops

parthkohli · Answer

@campbell_st Help please, I'm bad at sequences

campbell_st · Answer

there is an altenative formula for sum of an arithmetic series 

$$s _{n} = \frac{n}{2}[a + l]$$

this is a = 1st term l = (last term  term 7)

which is what parth has found..

campbell_st · Answer

so to use parth's informtion a = 26 l = 134

$$s _{7} = \frac{7}{2}(26 + 134)$$

campbell_st · Answer

either formula will give the same answer

parthkohli · Answer

So was I correct?

campbell_st · Answer

no parth... all you have done is found the 7th term... the question is asking for the sum of the 1st 7 terms...

campbell_st · Answer

my answer was 560

parthkohli · Answer

Oh yes, it said series.

campbell_st · Answer

you were part way to a solution

parthkohli · Answer

I didn't read the "TOTAL DISTANCE"

campbell_st · Answer

hope this helps algebra...