Sequences find a & d, find sum of first 60 terms.

[mattgad]

The sum of the first 2 terms of an arithmetic series is 47. The 30th term of this series is -62. Find first term and difference. Find sum of first 60 terms.

I have no idea where to start, can you point me in the right direction?

Thnaks.

 

[stapel]

I have no idea where to start.

Start from the definitions and the provided information.

Given:

. . . . .a₁ + a₂ = 47

By definition:

. . . . .a₂ = a₁ + d

Then:

. . . . .47 = a₁ + a₁ + d = 2a₁ + d

Given:

. . . . .a₃₀ = -62

By definition:

. . . . .a₃₀ = a₁ + 29d

Then:

. . . . .-62 = a₁ + 29d

This gives you two equations in two unknowns:

. . . . .2a₁ + 1d = 47
. . . . .1a₁ + 29d = -62

Solve the system for a₁ and d. Then answer the two questions.

Eliz.

 

[mattgad]

After getting:

-62 = U1 + 29d
47 = 2U1 + d

I'm still not sure what I would do to solve that as there are 2 unknowns in each question.

 

[pka]

Mattgad, Will you tell us something of your background?
The reason to ask that is, you have asked some rather advanced questions.
Yet you seem of lack some basic skills such as solving a simple system.
Are you doing a review of an advanced course?

 

[mattgad]

I'm actually taking the course, but due to the teacher being off a lot, and having lots of lessons cancelled, I am having to self teach.

 

[pka]

Well frankly, you will do yourself a great service if you take time out and review some basic, basic algebra. You are just beating you head against a brick wall not knowing the basics. We can solve the system for. But you will learn nothing from our doing it for you.

 

[mattgad]

Could you please let me know what type of operation I need to do to find the 2 values then. Is it simulataneous equations?

Thanks.

 

[pka]

If a+2b=7 and a-b=-2.
Multiply the second by 2: 2a-2b=-4.
Add that to the first: 3a=3, we eliminated the b.
Then a=1. Knowing that we see that b=3.
This is known as solving by elimination.

We could have taken the second and solve for a: a=b-2.
Substitute that in the first: (b-2)+2b=7.
Now solve for b.
That is known as solving by substitution.

 

[Denis]

http://people.hofstra.edu/faculty/Stefa ... it2_1.html

 

[mattgad]

Maybe it was too late to be doing it last night, but looked at again this morning and knew exactly how to use the simulataneous equations.