how many terms are there in the series 4+12+16+................+2916.
Since the nth term is 4n, and 2916 = 4*729 It appears that there are 729 terms.
the options given are a)5 b)6 c)27 d)35
Hmmm. I see I did make an error, since 4n would be
4,8,12,16,....
I have no idea how to get from 4 to 2916 in at most 35 terms, given the slow start. It does not appear exponential.
I could of course insert any required number of terms, but the rule would be awkward.
To determine the number of terms in the given series, we can use the formula for arithmetic progression. The formula for the nth term of an arithmetic progression is given by:
an = a + (n - 1)d
where "an" is the nth term, "a" is the first term, "n" is the number of terms, and "d" is the common difference.
In the given series, the first term "a" is 4 because it is the first number in the series. The common difference "d" can be found by subtracting the first term from the second term:
12 - 4 = 8
Now, we can use this information to find the number of terms "n". We want to find the last term of the series, which is given by:
an = 2916
Substituting the values, we get:
2916 = 4 + (n - 1)8
Simplifying the equation:
2916 - 4 = (n - 1)8
2912 = 8n - 8
2912 + 8 = 8n
2920 = 8n
Dividing both sides by 8:
n = 2920 / 8
n = 365
Therefore, there are 365 terms in the given series.