In an AP the 3rd term is 3 and the 5th term is -11 then find its 50th term
Answers
Step-by-step explanation:
a+2d= 3 eqn1
a+4d=-11 eqn2
subtract 2 from 1
⇒-2d= 14
⇒d= -7
a +2(-7)=12
⇒a=28
50th term
a+49d=28+49(-7)=
Answer:
-326
Step-by-step explanation:
Concept= Arithmetic Progression
Given=The 3rd and 5th term term of AP
To find= The 50th term
Explanation=
We have been given that in an AP the 3rd term is 3 and the 5th term is -11.
we need to find the 50th term
We know that in an Arithmetic Progression
the first number in stated as a and the second is a+d, a+2d and so on...
where d is the common different between the numbers.
the general term is calculated as aₙ= a+(n-1)d
The 3rd term is 3 so a₃= a+ (3-1)d = 3
3= a + 2d
The 5th term is -11 so a₅= a+(5-1)d= -11
-11 = a + 4d
Now on subtracting a₅ and a₃
a₅ - a₃ we get
-11 - 3 = a+4d - a-2d
-14 = 2d
d= -14/2
d= -7
therefore the common difference is -7
a₃ = a+ 2d= 3
a+ 2(-7) =3
a-14=3
a= 3+14
a=17
the first term is 17
50th term is a₅₀= a+(50-1)d
a₅₀= 17 + 49*(-7)
a₅₀= 17-343
a₅₀= -326
So the 50th term of AP is -326.
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