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1 answer:
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Answer:
a₈ = 37
Step-by-step explanation:
The given arithmetic sequence is: 3, 8, 13, 18, 23, . . .
The recursive formula for the sequence is:
Here, represents the
of the sequence.
And, represents the
of the sequence.
'+5' denotes that '5' is added to the term to get the
term. In other words, the difference between two consecutive numbers in the sequence is 5.
Now, we are asked to find a₈ i.e., n =8.
Substituting in the recursive formula we get: a₈ = a₍₈₋ ₁₎ + 5 = a₇ + 5.
So, to determine a₈ we need to know a₇. From the sequence we see that a₅ = 23.
⇒ a₆ = 23 + 5 = 28.
⇒ a₇ = 28 + 5 = 32.
⇒ a₈ = 32 + 5 = 37.
Therefore, the term of the sequence is 37.
Answer:
See explanation
Step-by-step explanation:
1 step:
n=1, then
So, for j=1 this statement is true
2 step:
Assume that for n=k the following statement is true
3 step:
Check for n=k+1 whether the statement
is true.
Start with the left side:
According to the 2nd step,
Substitute it into the
So, you have proved the initial statement