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Math Review: Arithmetic, Geometric Sequences, Induction, Binomial Coefficients, Study notes of Algebra

Math problems related to arithmetic and geometric sequences, finding common differences and ratios, sums, infinite series, and binomial coefficients. It includes exercises for finding terms and sums, as well as using mathematical induction to prove statements.

Typology: Study notes

Pre 2010

Uploaded on 08/10/2009

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koofers-user-4hs 🇺🇸

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Math 1521 AS ( College Algebra ),WEB
Some Review Problems Sheet #4
Topics: 17.1,17.2
1.a.Find the 13th term of the Arithmetic sequence :
2,6,10,14,18………………
b. Find the 9th term of the Geometric sequence:
2, ..........,.........
27
2
,
9
2
,
3
2
2. For the Arithmetic sequence
.............,.........3,8,13,18
a. Find the common Difference d.
b. Find the twenty-fourth term,
24
a
c. Find the sum, of the first 36 terms. ,
36
S
3. Find the first term, and the common difference, d, of the Arithmetic sequence
whose sum of the first 12 terms, is 246 and whose twelfth term , is 37.
,
1
a
,12
S12
a
4. For the Geometric sequence 49,7,1,……………………………….
i. Find the common ratio, r.
ii. Find the sixth term,
6
a
iii. Find the sum, of the first eight terms
8
S
iv. Find the infinite sum, if it exists.
S
pf3
pf4

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Math 1521 AS ( College Algebra ),WEB

Some Review Problems Sheet #

Topics: 17.1,17.

1.a.Find the 13

th term of the Arithmetic sequence :

b. Find the 9

th term of the Geometric sequence:

  1. For the Arithmetic sequence 18 , 13 , 8 , 3 ,......................

a. Find the common Difference d.

b. Find the twenty-fourth term, a 24

c. Find the sum, S 36 ,of the first 36 terms.

  1. Find the first term, and the common difference, d, of the Arithmetic sequence

whose sum of the first 12 terms, is 246 and whose twelfth term , is 37.

a 1 ,

S 12 (^) , a 12

  1. For the Geometric sequence 49,7,1,……………………………….

i. Find the common ratio, r.

ii. Find the sixth term, a 6

iii. Find the sum, S 8 of the first eight terms

iv. Find the infinite sum, S ∞if it exists.

  1. Consider the statement

2 S (^) n + + + nn + = n n + n

a. Write the statement Sk

b. Write the statement Sk + 2

  1. Use the Mathematical induction to prove that the statement

S n : 5 + 9 + 13 +............+^ (^4 n + 1 )^ = n (^2 n + 3 )

holds true for all positive integers n.

  1. Given the statement

: 1 + 2 + 3 + 4 +......................+ = n +

n S (^) n n

a. Write the statement S 1

b. Write the statement Sk

c. Write the statement Sk + 1

  1. Find (^) ⎟⎟

  1. Use Binomial coefficients to find the coefficient of in the expansion of

6 18 x y

2 2 12 x + y