ist and last term 1and11 respectively and their sum is 36. find number of terms
To find the number of terms in the sequence, we need to determine the common difference between consecutive terms.
Let's call the first term of the sequence "a" and the common difference between consecutive terms "d".
We are given that the first term, a, is 1 and the last term, which we can calculate using the formula for an arithmetic sequence, is 11.
Using the formula for the nth term of an arithmetic sequence:
last_term = a + (n - 1) * d
Substituting the given values, we have:
11 = 1 + (n - 1) * d
Next, we are given that the sum of the sequence is 36. We can use the formula for the sum of an arithmetic series to find the relationship between the first term, last term, and the number of terms:
sum = (n/2) * (first_term + last_term)
Substituting the given values, we have:
36 = (n/2) * (1 + 11)
36 = (n/2) * 12
36 = 6n
Now we have two equations:
11 = 1 + (n - 1) * d
36 = 6n
From the first equation, we can simplify it to:
10 = (n - 1) * d
10/d = n - 1
Substituting 10/d for n - 1 in the second equation, we have:
36 = 6(10/d)
36d = 60
d = 60/36
d = 5/3
Now we can substitute the value of d into the first equation to find n:
11 = 1 + (n - 1) * (5/3)
11 = 1 + (5/3)n - 5/3
33/3 = (5/3)n
11 = (5/3)n
11 * (3/5) = n
33/5 = n
n = 33/5
Therefore, the number of terms in the sequence is 33/5, which is equivalent to 6.6. However, since the number of terms must be a whole number, we round down to the nearest whole number. Therefore, the number of terms is 6.
Repeat without typos and with correct grammar.
Are we talking about arithmetic or geometric sequences or what?