Numbers and Sequences

If the sequence t₁,t₂,t_{3, .....} are in A.P then the sequence t_{6 ,}t_{12 ,}t_{18 , ....... is}

• a Geometric Progression

• an Arithmetic Progression

• neither an Arithmetic Progression nor a Geometric Progression

• a constant sequence

The value of ( 1³ + 2³ + 3³ + ..........+15³) - ( 1 + 2 + 3 + ........ +15) is

• 14400

• 14200

• 14280

• 14520

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

• 0, 1, 8

• 1, 4, 8

• 0, 1, 3

• 1, 3, 5

If the HCF of 65 and 117 is expressible in the form of 65m - 117, then the value of m is

• 4

• 2

• 1

• 3

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

• 2025

• 5220

• 5025

• 2520

The first term of an arithmetic progression is unity and the common difference is 4. Which of the following will be a term of this A.P.

• 4551

• 10091

• 7881

• 13531

If 6 times of 6th term of an A.P. is equal to 7 times the 7th term, then the 13th term of the A.P. is

• 0

• 6

• 7

• 13

An A.P. consists of 31 terms. If its 16^th term is m, then the sum of all the terms of this A.P. is

• 16 m

• 62 m

• 31 m

• 31/2 m

In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

• 6

• 7

• 8

• 9

If A = 2⁶⁵ and B =2⁶⁴ +2⁶³ +2⁶² + ... +2⁰ which of the following is true?

• B is 2⁶⁴ more than A

• A and B are equal

• B is larger than A by 1

• A is larger than B by 1