Question

If the sum of first 14 terms of an Ap Is 1050 and its first term is 10 find the 20th term in English medium

Answer 1

Answer:

Thus ,20th term is 257.

Answer 2

GIVEN THAT :-

• Sum of first 14 terms = 1050
• First term ( a ) = 10

TO FIND :-

• 20th term.

SOLUTION :-

We know that,

$\bullet\bf \ a_n=a+(n-1)d\\\\\bullet \ Sum \ of \ first \ n \ terms = \dfrac{n}{2}\times [ \ 2a+(n-1)d \ ]$

• Frist term = 10

        $\longrightarrow\sf a = 10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(1)$

• Sum of first 19 terms = 1050

       $\longrightarrow\sf \dfrac{14}{2}\times [ \ 2a+(14-1)d \ ] = 1050\\\\\longrightarrow \dfrac{14}{2}\times \ [ \ 2a+13d \ ]= 1050 \\\\\ \longrightarrow 7\times [ \ 2a+13d \ ] = 1050 \\\\\longrightarrow 2a+13d = 150 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(2)$

 Substitute the value of a in eq(2),

       $\longrightarrow\sf 2\times 10+13d= 150 \\\\\longrightarrow 20+13d= 150\\\\ \longrightarrow 13d = 130 \\\\\longrightarrow\bf d= 10$

 Common difference = 10

$\bullet$ 20th term = 10 + ( 20 - 1 ) 10

                   = 10 + 19 × 10

                   = 10 + 190

                  = 200