Write an equation for the nth term of the arithmetic sequence. then find a10.

10,0,−10,−

The equation to represent the nth term of the arithmetic sequence 10,0,−10,−20 is 20 - 10n

Given:

10,0,−10,−20

first term, a = 10

common difference, d = second term - first term

= 0 - 10

= -10

nth term = a + (n - 1) d

where,

n = number of terms

nth term = a + (n - 1) d

= 10 + (n - 1) -10

= 10 - 10n + 10

= 20 - 10n

nth term = 20 - 10n

Therefore, the equation to represent the nth term of the arithmetic sequence 10, 0, −10, −20 is 20 - 10n

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AP: 10, 0, -10, -20...

a = 10, d = -10

nth term of the AP = a + (n-1)d

= 10+ (n-1)-10

= 10 - 10n + 10

= 20 - 10n

a10 = 20-10(10)

= 20 - 100

= -80

Hope this helps!

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