Prove that in a sequence of numbers 49,4489,444889,44448889 in which every number is made by inserting 48-48 in the middle of previous as indicated, each number is the square of an integer.

If a_na_(n-1)a-(n-2),.,a_3,a_2,a-1 be a digit having a_1,a_2,a_3,…..a_n t unti, thens hundred places respectively. Then a_n a_(n-1) a_(n-2)….a_3a_2a_1= a_nxx1+a_2xx10^2+a_3xx10^3+…..+a_n10^(n-1) On the basis of above information answer the following question For a sequence {t_n},t_1=49, t_2= 4489, t_3=444889 in which every number is made by inserting 48 in the middle of the previous number. The for all nepsilonN, t_n is (A) square of an odd integer (B) divisible by 3 (C) divisible by 9 (D) none of these

If each number of a sequence is 4 more than the previous number, and the 3rd number in the sequence is 13, what is the 114th number in the sequence?

There is a certain sequence of positive real numbers. Beginning from the third term, each term of the sequence is the sum of all the previous terms. The seventh term is equal to 1000 and the first term is equal to 1 . The second term of this sequence is equal to

Three digit numbers in which the middle one is a perfect square are formed using the digits 1 to 9 Their sum is

In a certain sequence of numbers, each term after the 1 st term is the result of adding 2 to the previous term and multiplying that sum by 3 . If the 4th term in the sequence is 186 , what is the 2 nd term ?

A sequence is show below: 1,4,-4…. The first term is 1. Each even numbered term is 3 more than previous term and each odd numbered term after the first is (-1) times the previous term. What is the sum of the first 32 terms of the above sequence?

Find the middle term of the sequence formed by all three-digit numbers which leave a remainder 3, when divided by 4. Also find the sum of all numbers on both sides of the middle terms separately

Find the smallest square number which is divisible by each of the numbers 6, 9 and 15.

Which of the following compound statements is/are true? p : All fraction numbers are rational or all rational numbers are fraction q : Number of prime factors of 12 is 3 or number . of total factors is 6 r : Square of an integer is always positive or cube · of an integer may be negative or positive

i) Find the two consecutive positive even integers, the sum of whose square is 340. ii) Prove that there is a unique pair of consecutive odd positive integers such that sum of their squares is 290 find them. iii) Find all the numbers which exceeds their square root by 12. iv) Find the quadratic equation for which sum of the roots is 1 and sum of the squares of the roots is 13.