The 24th term is 152
Step-by-step explanation:
The formula of the nth term of an arithmetic sequence is:
[tex]a_n=a+(n-1)d[/tex] , where
The third term means n = 3
∵ [tex]a_3=a+(3-1)d[/tex]
∴ [tex]a_3=a+2d[/tex]
∵ [tex]a_3[/tex] = 5
- Equate the right hand sides of the third term
∴ a + 2d = 5 ⇒ (1)
The fifth term means n = 5
∵ [tex]a_5=a+(5-1)d[/tex]
∴ [tex]a_5=a+4d[/tex]
∵ [tex]a_5[/tex] = 19
- Equate the right hand sides of the fifth term
∴ a + 4d = 19 ⇒ (2)
Now we have a system of equations to solve it
Subtract equation (1) from equation (2) to eliminate a
∴ 2d = 14
- Divide both sides by 2
∴ d = 7
- Substitute the value of d in equation (1) to find a
∵ a + 2(7) = 5
∴ a + 14 = 5
- Subtract 14 from both sides
∴ a = -9
The twenty fourth term means n = 24
∵ a = -9 and d = 7
- Substitute the values of a and d in the formula of the nth term
∴ [tex]a_24=-9+(24-1)(7)[/tex]
∴ [tex]a_24=-9+(23)(7)[/tex]
∴ [tex]a_24=-9+161[/tex]
∴ [tex]a_24=152[/tex]
The 24th term is 152
Learn more:
You can learn more about the arithmetic sequence in brainly.com/question/7221312
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