Intermediate Algebra

# Practice Test

Intermediate AlgebraPractice Test

### Practice Test

In the following exercises, write the first five terms of the sequence whose general term is given.

320.

$a n = 5 n − 3 3 n a n = 5 n − 3 3 n$

321.

$a n = ( n + 2 ) ! ( n + 3 ) ! a n = ( n + 2 ) ! ( n + 3 ) !$

322.

Find a general term for the sequence, $−23,−45,−67,−89,−1011,…−23,−45,−67,−89,−1011,…$

323.

Expand the partial sum and find its value. $∑i=14(−4)i∑i=14(−4)i$

324.

Write the following using summation notation. $−1+14−19+116−125−1+14−19+116−125$

325.

Write the first five terms of the arithmetic sequence with the given first term and common difference. $a1=−13a1=−13$ and $d=3d=3$

326.

Find the twentieth term of an arithmetic sequence where the first term is two and the common difference is $−7.−7.$

327.

Find the twenty-third term of an arithmetic sequence whose seventh term is $1111$ and common difference is three. Then find a formula for the general term.

328.

Find the first term and common difference of an arithmetic sequence whose ninth term is $−1−1$ and the sixteenth term is $−15.−15.$ Then find a formula for the general term.

329.

Find the sum of the first 25 terms of the arithmetic sequence, $5,9,13,17,21,…5,9,13,17,21,…$

330.

Find the sum of the first 50 terms of the arithmetic sequence whose general term is $an=−3n+100.an=−3n+100.$

331.

Find the sum. $∑i=140(5i−21)∑i=140(5i−21)$

In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio.

332.

$14 , 3 , −8 , −19 , −30 , −41 , … 14 , 3 , −8 , −19 , −30 , −41 , …$

333.

$324 , 108 , 36 , 12 , 4 , 4 3 , … 324 , 108 , 36 , 12 , 4 , 4 3 , …$

334.

Write the first five terms of the geometric sequence with the given first term and common ratio. $a1=6a1=6$ and $r=−2r=−2$

335.

In the geometric sequence whose first term and common ratio are $a1=5a1=5$ and $r=4,r=4,$ find $a11.a11.$

336.

Find $a10a10$ of the geometric sequence, $1250,250,50,10,2,25,….1250,250,50,10,2,25,….$ Then find a formula for the general term.

337.

Find the sum of the first thirteen terms of the geometric sequence, $2,−6,18,−54,162,−486…2,−6,18,−54,162,−486…$

In the following exercises, find the sum.

338.

$∑ i = 1 9 5 ( 2 ) i ∑ i = 1 9 5 ( 2 ) i$

339.

$1 − 1 5 + 1 25 − 1 125 + 1 625 − 1 3125 + … 1 − 1 5 + 1 25 − 1 125 + 1 625 − 1 3125 + …$

340.

Write the repeating decimal as a fraction. $0.81—0.81—$

341.

Dave just got his first full-time job after graduating from high school at age 18. He decided to invest \$450 per month in an IRA (an annuity). The interest on the annuity is 6% which is compounded monthly. How much will be in Adam’s account when he retires at his sixty-fifth birthday?

342.

Expand the binomial using Pascal’s Triangle. $(m−2n)5(m−2n)5$

343.

Evaluate each binomial coefficient. $(81)(81)$
$(1616)(1616)$ $(120)(120)$ $(106)(106)$

344.

Expand the binomial using the Binomial Theorem. $(4x+5y)3(4x+5y)3$

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