Given the sequence 2,7, write an explicit
formula for the nth term, assuming a1=2.
2 given the sequence 2,7, find the sum of
the first 30 terms

Part 1)

Part 2) The sum of  the first 30 terms is 2,235

Step-by-step explanation:

Part 1)  write an explicit  formula for the nth term

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference

We can write an Arithmetic Sequence as a rule:

where

is the nth term

is the first term

n is the number of terms

d is the common difference

we have the sequence

we have

, ,

Find the common difference d

The common difference  is d=5

substitute in the formula

Part 2) Find the sum of  the first 30 terms

we know that

The formula to calculate the sum of an arithmetic sequence is

where

is the first term

n is the number of terms

d is the common difference

we have

substitute

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