How to find the nth term of an arithmetic sequence

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ACT Math › How to find the nth term of an arithmetic sequence

Questions 1 - 6

What is the th term in the following series of numbers: ?

148

Explanation

Notice that between each of these numbers, there is a difference of . This means that for each element, you will add . The first element is or . The second is or , and so forth... Therefore, for the th element, the value will be or .

Find the term of the following sequence:

$a_{10}=-111$

$a_{10}=-123$

$a_{10}=-99$

$a_{10}=-125$

$a_{10}=-113$

Explanation

The formula for finding the $n^{th}$ term of an arithmetic sequence is as follows:

where

= the difference between consecutive terms

= the number of terms

Therefore, to find the term:

$a_{10}=-3+(-12)(10-1)$

$a_{10}=-3+(-12)(9)$

$a_{10}=-3-108$

$a_{10}=-111$

If the first two terms of a sequence are $\small \pi$ and $\small 2\pi ^{2}$ , what is the 38th term?

$\small 2^{37}\pi ^{38}$

$\small 2\pi ^{38}$

$\small 2\pi ^{37}$

$\small 2^{37}\pi ^{37}$

$\small 2^{38}\pi ^{38}$

Explanation

The sequence is multiplied by $\small 2\pi$ each time.

Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is and whose ninth term is .

Explanation

Use the formula _a_n = _a_1 + (n – 1)d

_a_6 = a_1 + 5_d

_a_9 = a_1 + 8_d

Subtracting these equations yields

_a_6 – a_9 = –3_d

–7 – 8 = –3_d_

d = 5

_a_1 = 33

Then use the formula for the series; = –30

What is the rd term of the following sequence:?

Explanation

Notice that between each of these numbers, there is a difference of ; however the first number is , the second , and so forth. This means that for each element, you know that the value must be , where is that number's place in the sequence. Thus, for the rd element, you know that the value will be or .

If the first day of the year is a Monday, what is the 295th day?

Monday

Tuesday

Wednesday

Saturday

Explanation

The 295th day would be the day after the 42nd week has completed. 294 days/7 days a week = 42 weeks. The next day would therefore be a monday.

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