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Starrysoul100

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Given :-

  • Here, We have given the arithmetic sequence that is 4 , 10 , 16 , 22 ...and so on

To Find :-

  • We have to find the 68th term of the given AP

Let's Begin :-

Here, we have

  • Arithmetic sequence :- 4 , 10 , 16 , 22

We have to determine the 68th term of given AP

Therefore,

By using an formula that is,

[tex]\bold{\red{ an = a1 + (n - 1)d }}[/tex]

  • Here, a1 = first term
  • n = number of terms
  • d = common difference
  • an = term number

For finding common difference of AP

  • Subtract preceeding term from succeeding term
  • That is, a2 - a1

Here, common difference will be

[tex]\sf{ = 10 - 4 }[/tex]

[tex]\sf{ = 6 }[/tex]

Thus, The common difference of the given AP is 6

Now, Subsitute the given values in the above an formula :-

[tex]\sf{ an = 4 + (68 - 1)6 }[/tex]

[tex]\sf{ an = 4 + 67 {\times} 6 }[/tex]

[tex]\sf{ an = 4 + 402 }[/tex]

[tex]\sf{ an = 406 }[/tex]

Hence, The 68th term of the given AP is 406

Some basic details about AP

  • Arithmetic progression is the sequence of numbers that have same common difference between each succeeding and preceeding term.
  • For finding terms,
  • [tex]\bold{\red{ an = a1 + (n - 1)d }}[/tex]
  • For finding sum of terms
  • [tex]\bold{\red{ sn = }}{\bold{\red{\dfrac{n}{2}}}}{\bold{\red{ [2a + ( n - 1)d ]}}}[/tex]

The given Arithmetic Sequence is 4 , 10 , 16 , 22 , ... and we need to find the 68th term of the sequence , but let's recall that for any sequence in AP , the nth term is :

  • [tex]{\boxed{\bf{a_{n}=a+(n-1)d}}}[/tex]

Where , [tex]\bf a[/tex] is the first term of the sequence and [tex]\bf d[/tex] is the common difference ( [tex]{\bf{a_{n}-a_{n-1}}}[/tex] ) and [tex]\bf a_n[/tex] is nth term. So , now in this question , a = 4 and d = 10 - 4 = 6 . Now , rhe 68th term will be :

[tex]{:\implies \quad \sf a_{68}=4+(68-1)6}[/tex]

[tex]{:\implies \quad \sf a_{68}=4+(67)6}[/tex]

[tex]{:\implies \quad \sf a_{68}=4+402=406}[/tex]

Hence , the 68th term is 406

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