Determine the AP whose 3rd term is 5 and the 7th term is 9. - Vidyadip

Question

Determine the $AP$ whose 3rd term is $5$ and the $7th$ term is $9$.

✓

Answer

We have
$a_3 = a + (3 – 1) d = a + 2d = 5 ....(i)$
and $a_7 = a + (7 – 1) d = a + 6d = 9 .....(ii)$
Solution by substitution method: Now from equation (i), value of$ a = 5 - 2d .....(iii)$
put value of a from equation (iii) in equation (ii), we get
$5 - 2d + 6d = 9$
$4d = 9 - 5$
$4d = 4$
$d = 1$
now put value of d in equation (iii), we get
$a = 5 - 2\times1$
$a = 3$
Hence, the required AP is $3, 4, 5, 6, 7,...$

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