Question

For an Arithmetic Progressions , t4 = 20, t15 = 75,find tn .
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Answer 1

given in for an Arithmetic Progressions , t4 = 20, t15 = 75

the expression for the n'th term of the series in A.P is

Tn= a+(n-1)d

where a is the first term and d is the common difference

given T4= 20

a+(n-1)d=20

a+3d=20.......... eq.(1)

similarly ,

T15=75

a+(n-1)d=75

a+14d=75............eq.(2)

eq(2)-eq(1)

11d=55

d=5

substitute d=5 in eq(1)

a+3(5)=20

a=5

therefore Tn = a+(n-1)d= 5+(n-1)5 = 5n