The common difference of the AP is -2 ⇒ A
Step-by-step explanation:
The formula of the nth term of AP is [tex]a_{n}=a+(n-1)d[/tex] , where
- a is the first term
- d is the common difference between the consecutive terms
∵ The 8th term of an AP is -17
∴ n = 8 and [tex]a_{8}=-17[/tex]
- Substitute n by 8 and [tex]a_{n}[/tex] by -17 in the formula above
∴ -17 = a + (8 - 1)d
- Simplify the right hand side
∴ -17 = a + 7d
∵ The 14th term is -29
∴ n = 14 and [tex]a_{14}=-29[/tex]
- Substitute n by 14 and [tex]a_{n}[/tex] by -29 in the formula above
∴ -29 = a + (14 - 1)d
- Simplify the right hand side
∴ -29 = a + 13d
Now we have system of equations
a + 7d = -17 ⇒ (1)
a + 13d = -29 ⇒ (2)
Multiply equation (1) by -1 to eliminate a
-a - 7d = 17 ⇒ (3)
Add equations (2) and (3)
∴ 6d = -12
- Divide both sides by 6
∴ d = -2
The common difference of the AP is -2
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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