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Find the sum of the first 25 terms of the arithmetic sequence a1=100 and a25=220

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Answer:

look down

Explanation:

To find the sum of the first 25 terms of an arithmetic sequence, we can use the formula:

Sn = (n/2)(a1 + an)

Where:

Sn is the sum of the first n terms

n is the number of terms

a1 is the first term

an is the nth term

In this case, a1 = 100 and a25 = 220, so we need to find the value of n and an.

The formula to find the nth term (an) of an arithmetic sequence is given by:

an = a1 + (n - 1)d

Where d is the common difference.

We can calculate d using the values of a1 and a25:

d = (a25 - a1) / (25 - 1)

= (220 - 100) / (25 - 1)

= 120 / 24

= 5

Now, we can find the value of an:

an = a1 + (n - 1)d

220 = 100 + (25 - 1)5

220 = 100 + 24 * 5

220 = 100 + 120

220 = 220

The value of an is 220, which means the 25th term of the sequence is 220.

Now, substituting the values into the sum formula:

Sn = (n/2)(a1 + an)

= (25/2)(100 + 220)

= (25/2)(320)

= 25 * 160

= 4000

Therefore, the sum of the first 25 terms of the arithmetic sequence is 4000.

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