Sequences and S...

Find the value of $$'?'$$ in the series: $$12, 17, 15, ?, 18, 23, 21,....$$

Choose the missing number in the series: $$2, 2, 3, 4, 4,$$__$$, 6, 6, 7, 8, 8, 9....$$

Find the value of $$'x'$$ in the series: $$144, 169, x, 225, 256, 289$$.

The value of $$\displaystyle \tan { \alpha  } +2\tan { \left( 2\alpha  \right)  } +4\tan { \left( 4\alpha  \right)  } +...+{ 2 }^{ n-1 }\tan { \left( { 2 }^{ n-1 }\alpha  \right)  } +{ 2 }^{ n }\cot { \left( { 2 }^{ n }\alpha  \right)  } $$ is

Find the missing number in the pattern: $$2, 5, 8, 11,$$ __$$, 17, 20, 23, 26$$

Which number comes next?
$$5, 9, 13, 17, 21, 25, 29,...$$

The sum of $$24$$ terms of the following series $$2+4+6.....$$

$$2, 3,$$ __$$, 4, 4, 5, 6, 6, 6, 7, 7, 7...$$ What number should fill the blank?

Fill in the blank: $$62, 66, 63, 66, 64,$$ __$$, 65,....$$

Identify the missing integer: $$9, 45,$$ ____$$, 1125, 5625...$$