Question

determine the ap whose fifth term is 19 and the difference of the eight term form the thirteenth term is 20​

Answer 1

let a and d are first term and common difference of an A.P.

nth term =tn = a+(n-1)d........(1)

i) given t 5 =19

a+4d= 19......(2)

ii) difference of the eighth term from the thirteenth term is 20

t 13- t 8 = 20

a+12d-(a+7d)=20

a+12d-a-7d=20

5d =20

d=20/5

d=4

put d=4 in (2)

a+4d=19

a+4×4=19

a+16=19

a=3

therefore a=3 and d=4

required A.P. is

a, a+d, a+2d, a+3d, ........

3, 7, 11, 15, .......

Answer 2

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