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Find the sum of each of the following series:
(a) 2 + 7 + 12 + ...... +92

Sagot :

Subtomex0idn

Arithmetic Sequence

We can observe that we are adding 5 each time to the numbers, meaning this is an arithmetic sequence with a common difference d=5

Explicit Relation

We can establish the relation,

u(n)=u⁰+nd

where u(n) is the nth term (any term).

u⁰ is out first term (2)

d is the common difference (5)

u(n)=u⁰+nd

92 =2 +5n

5n =90

n =18

This sequence admits 19 terms since we start counting from 0 till 18.

Summation

S= number of terms/2 ×(u¹⁸+u⁰)

[tex]s = \frac{19}{2} \times (92 + 2)[/tex]

[tex]s = 9.5(94)[/tex]

[tex]s = 893[/tex]

That's ur answer :)

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