Question

The third term of an arithmetic progression is 9 while the 11th term is -7 find the first five terms of the a. p

Answer 1

Answer:

The first five terms of the A.P. are: 13, 11, 9, 7, 5, ...........  

Step-by-step explanation:

Given that,

Third term$\:(a_{3})\:$ of the A.P. is 9 and the 11th term$\:(a_{11})\:$ is -7

Let the first term of the A.P. be 'a' and common difference be 'd'.

We know that,

nth term of the A.P,

$a_{n}=a+(n-1)d\\Therefore,\:\\a_{3}=a+(3-1)d\\=>9=a+2d-----------------(i)\\and\\a_{11}=a+(11-1)d\\=>-7=a+10d-----------------(ii)$

On subtracting (ii)from (i), We get,

9 - ( - 7) = a + 2d - a - 10d

=>16 = -8d

=>d = -2

Putting the value of d= -2 in equation (i) we get,

9 = a + 2×(-2)

=>9 = a - 4

=> a = 9 + 4

=> a = 13

∴ Required A.P. has first term(a) = 13 and common difference (d) = -2.

Now, the first five terms of the A.P. are: 13, 11, 9, 7, 5, ...........  

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