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Bess [88]
3 years ago
11

Find the sum of the first 47 terms of the following series, to the nearest integer.

Mathematics
1 answer:
topjm [15]3 years ago
8 0

Answer:

The sum of the first 47 terms of the given series = 6016

Step-by-step explanation:

Given the sequence

13, 18, 23, ...

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

18-13=5,\:\quad \:23-18=5

As the difference between all the adjacent terms is the same.

so

d=5

a_1=13

Arithmetic sequence sum formula

n\left(a_1+\frac{d\left(n-1\right)}{2}\right)

Put the values

d=5

a_1=13

n=47

=47\left(13+\frac{5\left(47-1\right)}{2}\right)

=47\left(13+\frac{5\left(47-1\right)}{2}\right)

=47\left(13+115\right)

=47\cdot \:128

=6016

Thus, the sum of the first 47 terms of the given series = 6016

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