Question

_,24,_42... In arithmetic sequence some terms are missing.Find them​

Answer 1

Given:-

• Second term of an A.P = 24

• Fourth term of an A.P = 42

To Find:-

• Missing Terms i.e. First and Third terms

Formula Used:-

• ${\boxed{\bf{a_n=a+(n-1)d}}}$

Here,

• $\bf a_n=General\:Term$

• a = First term

• d = Common Difference

• n = No. of terms

Solution:-

As given,

• $\bf a_2=24\:and\:a_4=42$

Solving it,

$\sf :\implies\:a_n=a+(n-1)d$

$\sf :\implies\:a_2=a+(2-1)d$

$\sf :\implies\:a+d=24$

$\bf :\implies\:a=24-d$ ___ {1}

And,

$\sf :\implies\:a_4=a+(4-1)d$

$\sf :\implies\:42=24-d+3d$

$\sf :\implies\:42=24+2d$

$\sf :\implies\:2d=42-24$

$\sf :\implies\:2d=18$

$\sf :\implies\:d=\dfrac{18}{2}$

$\bf :\implies\:d=9$

Putting value of d in {1},

$\sf :\implies\:a=24-9$

$\bf :\implies\:a=15$

Hence,

• First Term = a = 15

• Third Term = a+2d = 15 + 2×9 = 33

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