Question

in an arithmetic sequence fourth term is 20 and tenth term is 56
a) find first term and common difference
b) write the algebraic form
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Answer 1

Answer: for an A.P. :t4 =20 and t10=56   to find:t1=?                                          tn  =a+(n-1)d                                                                                                             ∴t4  =a+(4-1)

∴20=a+3d

∴a+3d=20      ----(1`)

also t10= a+(10-1)d

56 =a+9d  

a+9d=56     ----(2)

subtracting  (1) from(2),

a  +  9d  =56

a  +   3d  =20

(-)      (-)    (-)

___________

        6d  =36

d=36/6

d=6

substituting d=6 in eq (1)

a+3d=20

a+3*6 =20

a+18=20

a=20-18

a=2

here,a=2;d=6,t1=?

∴t1=a=2    d=6