Question
Determine the arithmetic progression whose 3rd term is 5 and 7th term is 9.
✓
Answer
For an A.P
$t_3=5$
$\Rightarrow a+2 d=5$
And $t_7=9$
$\Rightarrow$ a + 6d = 9 ....(ii)
Substracting (i) from (ii) we get
4d = 4
$\Rightarrow$ d = 1
Substituting d = 1 in (i) we get
$a+2 \times 1=5$
$\Rightarrow$ a = 3
Thus the required A.P = a, a + d, a + 2d. a + 3d, ...
= 3, 4, 5, 6, .....
$t_3=5$
$\Rightarrow a+2 d=5$
And $t_7=9$
$\Rightarrow$ a + 6d = 9 ....(ii)
Substracting (i) from (ii) we get
4d = 4
$\Rightarrow$ d = 1
Substituting d = 1 in (i) we get
$a+2 \times 1=5$
$\Rightarrow$ a = 3
Thus the required A.P = a, a + d, a + 2d. a + 3d, ...
= 3, 4, 5, 6, .....
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