Question

If the sum of first 14 terms of an arithmetic progression is 1050 and it's fourth term is 40, find its 20th term?
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Answer 1

Answer:

Given

FourthtermofaA.P(a 4 )=40

20 th termofaA.P(a 20 )=?

Sum of first 14 terms S 14 =1050

Step-by-step explanation:

AccordingtotheQuestionnow:

⟹a n =a+(n−1)d

⟹a 4 =a+(4−1)d

:⟹40=a+3d...(i)

⇢S= 2/n{2a+(n−1)d }

⇢S 14 = 2/14{ 2a+(14−1)d }

⇢1050= 2/14 { 2a+(14−1)d }

⇢1050= 7 { 2a+13d }

⇢ 7/1050 =2a+13d

⇢150=2a+13d

⇢75=a+6.5d...(ii)

Dividing whole eq n by2

Now,from eqn

(i)and eqn

(ii)weget:

⟶75−40=a+6.5d−(a+3d)

⟶35=a+6.5d−a−3d

⟶35=6.5d−3d

⟶35=3.5d

⟶d= 3.5/35

⟶ d=10

Substituting the value of d=10 in eqn

(i)weget:

⇝40=a+3d

⇝40=a+3×10

⇝40=a+30

⇝a=40−30

⇝ a=10

† 20th term of a A.P

↦a n =a+(n−1)d

↦a 20 =10+(20−1)×10

↦a 20 =10+19×10

↦a 20 =10+190

==>  a20 = 200

Answer 2

Step-by-step explanation:

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