Question

The 3rd term and 7th term of ap is 14 and -2 which term of ap will be -14

Answer 1

difference = -4

a=22

tn=a+(n-1) d

-14=22+n-4

-14=18+n

-14-n=18

-n=32

n=-32

Answer 2

Finding the term in AP:

Step-by-step explanation:

$\ Given \ values:\\\\\ 3^{rd} \ term \ = (a+2d) = 14.....(i)\\\\7^{th} \ term \ = (a+6d) =-2......(ii)\\\\\ Solution: \\\\\ Subtract \ equation \ (ii) \ from \ equation (i) \\\\\ a+6d =-2\\\ - \\\ a+2d = 14 \\\\\rightarrow 6d - 2d =-2 -14\\\\\rightarrow 4d =- 16\\\\\rightarrow d = - 4\\\\\ put \ the \ value \ of \ d \ in \ equation \ (i) \\\\\ equation: \\\\\rightarrow a+2d = 14 \\\\\rightarrow a+2 \times -4 = 14 \\\\\rightarrow a-8 = 14 \\\\\rightarrow a = 14+8$

$\rightarrow a = 22$

$\ Finding \ term \\\\\ a= 22\\\\\ d = - 4\\\\\ t_n = -14\\\\\ Formula: \\\\\ t_n= a+(n-1)d\\\\\rightarrow -14= 22+(n-1)(-4)\\\\\rightarrow -14= 22-4n+4\\\\\rightarrow -14= 26-4n\\\\\rightarrow 4n= 26+14\\\\\rightarrow 4n= 40\\\\\rightarrow n= 10$

Test value:

$\ 10^{th} \ term = \ (a+9d) = 22+9(-4) \ = 22-36 \ = \ -14$

Learn more:

• Find the term: https://brainly.in/question/11842979