Question

Find the 20th term of an AP whose 3rd term is 7 and the seventh term exceeds three times the 3rd term by 2. Also find its nth term(an).

Answer 1

Hope u like my process
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Formula to be used
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=>Tn = a + (n-1)d

where

Tn = nth term

a = first term

d = difference

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Given
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=> 3rd term = 7

=> a +(3-1)d = 7

=> a + 2d = 7____(1)

Also

=> 7th term = 3(7) +2 = 21+2 = 23

=> a + (7-1)d = 23

=> a + 6d = 23_____(2)

Subtracting equation (1) from (2)
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=> a+ 6d - a - 2d = 23-7

=> 4d = 16

=> d = 16/4 = 4

Putting the value of d in equation (1)
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=> a+ 2(4) = 7

=> a = 7-8 = -1

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=> 20th term of AP = a +(20-1)d

= -1 + 19×4 = -1 +76 = 75
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=> nth term = a + (n-1)d

= -1 + 4n -4 = 4n -5
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Hope this is your required answer

Proud to help you.

Answer 2

A3=7

a+2d=7.........(1)

a7=3(a3)+2

a+6d=3(7)+2

a+6d=23........(2)

subtracting

a+2d=7

a+6d=23

-4d=-16

d=16/4

d=4

put in equation 1

a+2(4)=7

a+8=7

a=-1

a 20=a+19d

=-1+19(4)

=-1+76

=75

so, 20th term of an AP is 75