Question

the 7th term of an A.P.is -4 and its 13th term is -16 find the A.P .?

Answer 1

(a+6d)=7th term
(a+6d)=-4 & (a+12d)=-16
now solve the equations you will get
-6d=12
d=-2
putting the value of d in any equation
we get. a=8
Now apply the formula
a+(n-1)×d
so A.P=8,6,4,2,0,-2,-4,-6,-8,-10,-12,-14,........ and so on

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Answer 2

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$Given \: that : \: \\ \\ 7th \: term \: = - 4 \\ a + 6d = - 4 = = > (1) \\ \\ 13th \: term \: = - 16 \\ a + 12d = - 16 = = > (2) \\ \\ Now ,\: solve \: the \: equation \: (1) \: and \: (2) \\ \\ From \: eq.(1) \\ a + 6d = - 4 \\ a = - 4 - 6d \\ \\ Putting \: \: the \: value \: of \: a \: in \: eq.(2) \\ a + 12d = - 16 \\ = > ( - 4 - 6d) + 12d = - 16 \\ = > 6d = - 12 \\ = > d = - 2 \\ \\ Putting \: the \: value \: of \: "d "\: in \: eq.(1) \\ = > a = - 4 - 6d \\ = > a = - 4 - 6(-2) \\ = > a = 8\\ \\ So ,\: First \: term \: is \: 8 \: \\ Common \: difference \: =- 2$

So, a2 = a+ d
=> a2 = 8-2
=> a2 = 6

a3 = a2 + d
=> a3 = 6 +( -2)
=> a3 = 4

We get A.P. : 8 ,6,4,2,0,-2,-4....

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