Question

determine the Ap whose 3rd term is 5 and 7th term is 9​

Answer 1

$\underline{\underline{\mathfrak{\Large{Solution : }}}}\\ \\ \underline {\textsf {We have,}}\\ \\ \sf\: a_3 = a + (3 - 1)d \\ \\ \sf\implies\: a + 2d = 5 \: \: \: ....... (1) \\ \\ \sf\: a_7 = a + (7 - 1)d \\ \\ \sf\implies\:a + 6d = 9 \: \: \: ...... (2) \\ \\ \sf\: Solving\: Pair\: of \:equations\:(1)\:and\:(2)\: We\:get \\ \\ \sf\: a = 3 , d = 1 \\ \\ \sf\:Hence\:the\:required \:A.P\:is\:3,4,5,6,7,..... \\ \\ \\ \underline {\textsf {Formulas used :}} \\ \\ \sf\: 1) \: \:S_n = a + (n - 1)d$

Answer 2

Step-by-step explanation:

nth term of an AP an = a + (n - 1) * d

(i)

3rd term of the AP is 5.

a₃ = 5

a + (3 - 1) * d = 5

a + 2d = 5

(ii)

7th term of the AP is 9.

a₇ = 9

a + (7 - 1) * d = 9

a + 6d = 9

On solving (i) & (ii), we get

a + 2d = 5

a + 6d = 9

----------------

     -4d = -4

         d = 1

Substitute d = 1 in (i)

a + 2d = 5

a + 2 = 5

a = 3

Thus, the AP is 3,4,5,6......

Hope it help you.