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Can someone help pls????
detail for me as well​

Can someone help pls???? detail for me as well​-example-1
User Dekts
by
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2 Answers

5 votes

Answer:

∑ (i = 1 to 5) (3·i)

= 3·∑ (i = 1 to 5) (i)

= 3·(1 + 2 + 3 + 4 + 5)

= 3·15

= 45

User Omarzl
by
8.9k points
4 votes

Explanation:

the easy straight forward method is to simply sum up the 5 terms.

you know that this symbol just means "sum", right ?

and that the index variable is "running" from 1 to 5.

so, you have to sum up

3×1 + 3×2 + 3×3 + 3×4 + 3×5 = 3 + 6 + 9 + 12 + 15 = 45

now, if you want it done via a summary formula to add the first n terms of an arithmetic sequence, like in this case

a1 = 3

an = an-1 + 3 = a1×n = 3n

then

the sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ).

it simply means : first plus last term added up n/2 times.

why ?

because a1 + an = a2 + an-1 = a3 + an-2 = ...

we get n/2 times such part sums.

so, in our case, n = 5, and we get

(3 + 3×5)×5/2 = (3 + 15)×5/2 = 18×5/2 = 9×5 = 45

User Stellasia
by
9.1k points

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