the 9th and 19th terms of a series of a.p are respectively 35 and 75.find the series and 20th term
amitnrw:
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a9=35
35=a+8d.....(1)
a19=75
75=a+18d...(2)
Now, on subtracting equation 1 from2
75-35=a+18d-a-8d
40=10d
d=40/10=4
substitute this in equation 1
35=a+8(4)
35-32=a
a=3
So,AP is 3,7,11......
a20=a+19(d)
a20=3+19(4)
a20=3+76=79
35=a+8d.....(1)
a19=75
75=a+18d...(2)
Now, on subtracting equation 1 from2
75-35=a+18d-a-8d
40=10d
d=40/10=4
substitute this in equation 1
35=a+8(4)
35-32=a
a=3
So,AP is 3,7,11......
a20=a+19(d)
a20=3+19(4)
a20=3+76=79
19th term + 4(d) = 20th term could be simpler solution
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