Question

find the equation of the arithmetic sequence in which t(5)=40 and t(10)=70.

Answer 1

The equation of the arithmetic sequence in which  t(5)=40 and t(10)=70 is tₙ = 10 + 6n

How to find the equation of an arithmetic sequence?

The equation of an arithmetic sequence can be represented as follows;

tₙ = a + (n  -1)d

where

• a = first term
• d = common difference
• n = number of terms

Hence,

70 = a + 9d

40 = a  + 4d

30 = 5d

d = 30 / 5

d = 6

Therefore,

40 = a + 4(6)

40 - 24 = a

a = 16

Hence, the equation is as follows:

tₙ = 16 + (n - 1)6

tₙ = 16 + 6n - 6

tₙ = 16 - 6 + 6n

tₙ = 10 + 6n

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