3 years ago

2 to the power of 14

Mathematics

2 answers:

mrs_skeptik [129]3 years ago

6 0

2 to the power of 14 means 2^14.
That would be 16384.

vlada-n [284]3 years ago

5 0

The answer is 16,384. Basically you need to multiply 2 fourteen times.

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$a_1=-20,\ a_3=-15\\\\2d=a_3-a_1\to 2d=-15-(-20)\to2d=-15+20\to2d=5\to d=2.5\\\\a_n=a_1+(n-1)d\to a_n=-20+(n-1)(2.5)=-20+2.5n-2.5=2.5n-22.5\\\\a_2=2.5(2)-22.5=5-22.5=-17.5\\\\a_4=2.5(4)-22.5=10-22.5=-12.5\\\\a_6=2.5(6)-22.5=15-22.5=-7.5$

n | 1 | 2 | 3 | 4 | 5 | 6 |

f(n)| -20 | -17.5 | -15 |-12.5| -10 | -7.5 |

First term: -20 Common Difference: 2.5

Explicit Rule: $a_n=2.5n-22.5$ Recursive Rule: $a_1=-20,\ a_n=a_{n-1}+2.5$

$a_1=123,\ a_2=131\\\\d=a_2-a_1\to d=131-123=8\\\\a_n=a_1+(n-1)d\to a_n=123+(n-1)(8)=123+8n-8=8n+115\\\\a_3=8(3)+115=24+115=139\\\\a_5=8(5)+115=40+115=155\\\\a_6=8(6)+115=48+115=163$