Question

the second term of the ap is 13 and 5th term is 25,then 7th term is​

Answer 1

AnswEr:

Given-

$\implies\sf a_{2} = a + d$

$\implies\sf a_{5} = a + 4d$

$\implies\sf a + d = 13 \:\:\:\:\:\:\;\;....[Equation \;1]$

$\implies\sf a + 4d = 25 \:\:\:\:\:\:\;\;....[Equation \;2]$

$\rule{150}2$

$\small\bold{\underline{\sf{\purple{From\; Equations\; (1) \:\&\;(2)}}}}$

$\implies\sf a + 4d = 25$

$\implies\sf a + d = 13$

$\implies\sf 3d = 12$

$\implies\sf d =\cancel\dfrac{12}{3}$

$\implies\boxed{\sf{\blue{d\:=\;4}}}$

$\small\sf{Substituting\:the\: Value\:of\:x\:in\; Equation\;(1)}$

$\implies\sf a + d = 13$

$\implies\sf a + 4 = 13$

$\implies\sf a = 13 - 4$

$\implies\boxed{\sf{\blue{a\:=\;9}}}$

$\rule{150}2$

$\small\sf{Now,\: Finding\: 7th\: Term}-$

$\implies\sf a_{7} = a + 6d$

$\implies\sf a_{7} = a + 6(4)$

$\implies\sf a_{7} = 9 + 24$

$\implies\boxed{\sf{\pink{a_{7} \:=\: 33}}}$

$\small\bold{\underline{\sf{Hence,\:7th\;Term\:of\;the\;Given\;AP\;is \;33.}}}$

Answer 2

GIVEN:

Second term of an AP = 13

Fifth term of AP = 25

TO FIND:

Seventh term of the AP

SOLUTION:

Second term:

a + d = 13 -----(1)

Fifth term:

a + 4d = 25 ----(2)

After subtracting both eq -(1) & (2)

==> -3d = -12

==> d = 12/3

==> d = 4

Common Difference = 4

Substitute (d) in eq - (1) to find a

==> a + (4) = 13

==> a = 13 - 4

==> a = 9

First term = 9

Seventh term of AP:

==> a + 6d

==> (9) + 6(4)

==> 9 + 24

==> 33

Therefore, seventh term of AP is 33.