How to find the nth term of an arithmetic sequence - ACT Math
Card 0 of 6
Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is 
and whose ninth term is 
.
Find the sum of the first fifteen terms in an arithmetic sequence whose sixth term is
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
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
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If the first day of the year is a Monday, what is the 295th day?
If the first day of the year is a Monday, what is the 295th day?
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.
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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If the first two terms of a sequence are 
and 
, what is the 38th term?
If the first two terms of a sequence are
The sequence is multiplied by 
each time.
The sequence is multiplied by
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Find the 
term of the following sequence:
Find the
The formula for finding the 
term of an arithmetic sequence is as follows:
where
= the difference between consecutive terms
= the number of terms
Therefore, to find the 
term:
The formula for finding the
where
Therefore, to find the
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What is the 
th term in the following series of numbers: 
?
What is the
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 
.
Notice that between each of these numbers, there is a difference of
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What is the 
rd term of the following sequence:
?
What is the
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 
.
Notice that between each of these numbers, there is a difference of
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