Question

An Ap consists of 50 terms of which 3rd term is 12 and the last term is 106 .Find the 29th term

Answer 1

Answer:

Step-by-step explanation:

an=106

a+(n-1)d=106

a3=12

a+2d=12

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

$\textbf{\underline{First\;term\;be\;p}}$

$\textbf{\underline{Common\; Difference\;be\;d}}$

Also,

n = 50

$\tt{\rightarrow p_{3}=12}$

$\tt{\rightarrow p_{50}=106}$

Now,

$\tt{\rightarrow p_{3}=12}$

p + 2d = 12 ..... (1)

$\tt{\rightarrow p_{50}=107}$

p + 49d = 106 ..... (2)

${\boxed{\sf\:{Subtracting\;(1)\;from\;(2)}}}$

47d = 94

$\tt{\rightarrow d=\dfrac{94}{47}}$

d = 2

${\boxed{\sf\:{Put\;the\;value\;of\;d\;in\;(1)}}}$

p + 2(2) = 12

p + 4 = 12

p = 12 - 4

p = 8

Therefore

${\boxed{\sf\:{p_{29}=a+28d}}}$

= 8 + 28(2)

= 64

$\Large{\boxed{\sf\:{Hence\;29^{th}\;term\;is\;64}}}$