lf 6ⁿ is a number such that n is a natural number. Check whether is any value of n \(\in\) N for which 6ⁿ is divisible by 7.

Find the H.C.F. and L.C.M of 100 and 190 by fundamental theorem of arithmetic

Write the H.C.F. of smallest composite number and the smallest Prime number

The traffic lights at three different road crossings change after every 48 sec, 72 sec and 108 sec respectively. If they all change simultaneously at 8.20 am, then at what time will they again change simultaneously?

\(\text { Does } 7 \text { divides }\left(2^{29}+3\right) ?\)

What is the remainder when 3²⁰⁹ + 5⁹ is divided by 8?

write the first three terms of the sequence defined by \(a_{n}=(-1)^{n-1}, 2^{n}\)

What is the 15^th term of the sequence defined by \(a_{n}=\frac{n(n-3)}{n+4} ?\)

Write the general term of the sequence \(\frac{-1}{2}, 0, \frac{3}{2}, \frac{8}{2}, \ldots\)

Find the n^th term of the sequence 5, 8, 11,...

Find the first three terms of \(a_{n}=\frac{2 n-3}{6}\)

\(\text {If } 2 \mathrm{x}, \mathrm{x}+10,3 \mathrm{x}+2 \text { are in A.P. Find } \mathrm{x} \text {. }\)

Find four terms of an A.P. whose sum is 20 and the sum of whose squares is 120

Which term of the A.P. -1, 3 ,7, 11 .... is.95?

If s_n the sum of first n terms of an A.P. is given by s_n = 5n² + 3n.Then find the n^th term.