In sequence 5,9,13 find the sum of the first 18th term given that the 18th term is 92
The sequence 5, 9, 13 is an arithmetic sequence with a common difference of 4. To find the 18th term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
Where:
an = 18th term
a1 = 1st term = 5
d = common difference = 4
a18 = 5 + (18-1)4
a18 = 5 + 17*4
a18 = 5 + 68
a18 = 73
Given that the 18th term is 92, we have:
92 = a18
Now, we can find the sum of the first 18 terms of the sequence using the formula for the sum of an arithmetic series:
Sn = (n/2)(a1 + an)
Where:
Sn = sum of the first n terms
n = number of terms = 18
a1 = 1st term = 5
an = 18th term = 92
S18 = (18/2)(5 + 92)
S18 = 9(97)
S18 = 873
Therefore, the sum of the first 18 terms of the sequence is 873.