Final answer:
To find the nth term of the given sequence, we can use the formula an =a1 +(n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.
Step-by-step explanation:
The given sequence is 11, 781, 1551, 2321, 3091. To find the nth term of this sequence, we need to observe the pattern. If we subtract 10 from each number, we get the sequence 1, 771, 1541, 2311, 3081. Now, if we subtract the previous number from the current number in this new sequence, we get the sequence 770, 770, 770, 770. Since this difference remains constant, we can conclude that the common difference in the original sequence is also 770. To find the nth term, we can use the formula:
an = a1 + (n-1)d
Where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference. In this case, a1 = 11 and d = 770. Plugging these values into the formula, we get:
an = 11 + (n-1)770
This is the formula to find the nth term of the given sequence.