Question

Find 20th term of AP, where the 3rd term is 7 and 7th term exceeds 3 times the 3rd term by 2. Also find the nth term? Please provide the answer at the earliest.

Answer 1

let a is the first term and d is the common difference of AP
according to question ,
3rd term=7
a+(3-1) d=7
a+2d=7---------------(1)

also ,
7th term =3 x 3rd term +2
a+(7-1) d=3 (a+2d) +2
a+6d=3a+6d +2

a=-1 put value of a in equation (1)
d=4

now 20th term =-1+19 x 4=75
and nth term =a+(n-1) d=-1+4n-4=4n-5

Answer 2

20th term is 58 and nth term is (3n^2-n)/2
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