What is the sum of the arithmetic sequence 22, 13, 4 … if there are 28 terms?
It looks like 9 is being subtracted from the previous term. The sum will definitely be negative. Does that help?
What is the sum of the arithmetic sequence 22, 13, 4 … if there are 28 terms?
sum of 28 terms = 28/2[2*22+27*9]
= 14 [44=243]
= 14*287
= 4014
.. Sum of n terms = n/2[2a+(n-1)d]
Where n= number of terms
a= First term , d= Common difference
To find the sum of an arithmetic sequence, you can use the formula:
S_n = (n/2) * (a_1 + a_n)
Where:
- S_n is the sum of the first n terms
- n is the number of terms
- a_1 is the first term
- a_n is the last term
In this case, the first term (a_1) is 22, and the number of terms (n) is 28. We need to find the last term (a_n).
To find the common difference (d) of the arithmetic sequence, we can calculate the difference between two consecutive terms:
d = a_2 - a_1
In this case, a_2 is 13 and a_1 is 22, so we have:
d = 13 - 22 = -9
Now, we can find the last term (a_n) using the formula:
a_n = a_1 + (n - 1) * d
Substituting the values we know:
a_n = 22 + (28 - 1) * (-9)
= 22 + 27 * (-9)
= 22 - 243
= -221
Now that we have the first term (a_1 = 22), the last term (a_n = -221), and the number of terms (n = 28), we can substitute these values into the formula:
S_n = (n/2) * (a_1 + a_n)
= (28/2) * (22 + (-221))
= 14 * (-199)
= -2,786
Therefore, the sum of the arithmetic sequence 22, 13, 4... with 28 terms is -2,786.