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Question

Consider the sequence, 3,9,15,21

1. Find the sum of the first N terms
2. Find the N^th term

Consider the sequence, 5,10,20,40

1. Find the N^th term
2. Find the sum of the first N terms

Find the Sum of the sequence 6+10+14+18+.....+106

Find the Sum of the sequence 3+5+5/4+5/8+5/16+...

A brick stair cas has 30 steps. The bottom step requires 150 bricks, Each successive step requires 4 less bricks than the prior step.

1. How many bricks required for the 17th step?
2. How many total bricks required to build the staircase?

Answer 1

it's an arithmetic sequence with common difference = 6 = d

a1 =3

a2 =3+(2-1)(6)

a3 = 3+(3-1)6

an= a1 + (n-1)d = 3 +6(n-1) = 3 +6n-6 = 6n-3

an = 6n-3

sum of the 1st n terms of an arithmetic series is n(n+1)/2 first discovered by Gauss, when he was about 3 or in the 3rd grade when a math instructor gave him the problem how to add up all the numbers 1 to 100. He instantly gave the answer. Gauss was a child progeny, up there with Mozart composing music at a similarly early age. They put the rest of us to shame.

5,10,20, 40 is a geometric sequence, with each term twice the previous term. a common ratio, r, =2

nth term is a1 + r^(n-1)

a1 = 5

a2 = 5+5^(2-1) =5+5=10

sum of n terms is a1(1-r^n)/(1-r)

sum of 5 +10, with two terms, n=2, is 5(1-2^2)/(1-2) = 5(-3)/-1 = 15