Question 25

Given below are two statements
Statement I: In the sequence of numbers 30, 90, 182, 306, 462,P........ . the term P is 650.
Statement II : There are 8 digits in $$9^{8}$$ when it is expressed in decimal form.
In light of the above statements, choose the correct answer from the options given below

Solution

We have :
30, 90, 182, 306, 462,P.
Now 90-30 =60  (1)
182-90 = 92 (2)
306-182 = 124   (3)
462 -306 = 156  
If you observe , the first difference of the terms form an arithmetic progression
So we can say the next term will be
462 +156+32 = 462 +188 = 650
So P is 650
So statement 1 is true .
Taking statement 2 :
we get 9^8
Now number of digits = [log9^8 +1]
we get [8log9+1]= 8
so number of digits in 9^8 is 8


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