asked 215k views
3 votes
The first term in an arithmetic series is 2, while the sum of the first 8 terms of the series is 1472. What is the 8th term in the series?

A) 314
B) 418
C) 262
D) 366

The first term in an arithmetic series is 2, while the sum of the first 8 terms of-example-1

1 Answer

4 votes
To solve this problem, we'll need to use the formula for the sum of an arithmetic series:

S_n = n/2(2a + (n-1)d)

where S_n is the sum of the first n terms of the series, a is the first term, and d is the common difference between terms.

We're given that a = 2 and n = 8, and we know that the sum of the first 8 terms is 1472. So we can plug in these values and solve for d:

1472 = 8/2(2(2) + (8-1)d)
1472 = 4(4 + 7d)
1472 = 16 + 28d
1456 = 28d
d = 52

Now that we know the common difference is 52, we can use the formula for the nth term of an arithmetic series to find the 8th term:

a_8 = a + (n-1)d
a_8 = 2 + (8-1)52
a_8 = 2 + 364
a_8 = 366

So the 8th term in the series is D) 366.
answered
User Pierre Arlaud
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