Answer:
Common difference(d) [tex]a_{52}[/tex]
(21) -10 -548
(22) -7 -323
(23) 10 547
(24) -100 -5118
Step-by-step explanation:
Let the common difference be denoted by 'd'.
Also the nth difference of an arithmetic sequence is given by: [tex]a_{n}=a_{1}+(n-1)\times d[/tex]
(21)
We are given a recursive formula as:
[tex]a_{n}=a_{n-1}-10[/tex]
The first term is given by:
[tex]a_{1}=-38[/tex]
The common difference for an arithmetic sequence is given by:
[tex]a_{n}-a_{n-1}[/tex]
Hence, here we have the common difference as:
[tex]d=-10[/tex]
The nth term of an arithmetic sequence is given by:
[tex]a_{n}=a_{1}+(n-1)\times d[/tex]
Here [tex]a_{1}=-38[/tex] and [tex]d=-10[/tex].
Hence, [tex]a_{52}=-38+(52-1)\times (-10)[/tex]
Hence, [tex]a_{52}=-548[/tex]
(22)
[tex]a_{n}=a_{n-1}-7[/tex]
[tex]a_{1}=34[/tex]
The common difference for an arithmetic sequence is given by:
[tex]a_{n}-a_{n-1}[/tex]
Hence, here we have the common difference as:
[tex]d=-7[/tex]
Here [tex]a_{1}=34[/tex] and [tex]d=-7[/tex].
Hence, [tex]a_{52}=34+(52-1)\times (-7)[/tex]
Hence, [tex]a_{52}=-323[/tex]
(23)
[tex]a_{n}=a_{n-1}+10[/tex]
[tex]a_{1}=37[/tex]
The common difference for an arithmetic sequence is given by:
[tex]a_{n}-a_{n-1}[/tex]
Hence, here we have the common difference as:
[tex]d=10[/tex]
Here [tex]a_{1}=37[/tex] and [tex]d=10[/tex].
Hence, [tex]a_{52}=37+(52-1)\times (10)[/tex]
Hence, [tex]a_{52}=547[/tex]
(24)
[tex]a_{n}=a_{n-1}-100[/tex]
[tex]a_{1}=-18[/tex]
The common difference for an arithmetic sequence is given by:
[tex]a_{n}-a_{n-1}[/tex]
Hence, here we have the common difference as:
[tex]d=-100[/tex]
Here [tex]a_{1}=-18[/tex] and [tex]d=-100[/tex].
Hence, [tex]a_{52}=-18+(52-1)\times (-100)[/tex]
Hence, [tex]a_{52}=-5118[/tex]
