Question

the sum of first 14 terms of an AP is 1078 and its first term is 12 then its 20th term is

Answer 1

S O L U T I O N :

$\bf{\large{\underline{\bf{Given\::}}}}}$

The sum of first 14 terms of an A.P. is 1078 & it's first term is 12.

$\bf{\large{\underline{\bf{To\:find\::}}}}}$

The 20th term.

$\bf{\large{\underline{\bf{Explanation\::}}}}}$

We know that formula of the sum of an A.P;

$\boxed{\bf{S_n=\frac{n}{2} \bigg[2a+(n-1)d\bigg]}}}}$

A/q

$\longrightarrow\rm{1078=\cancel{\dfrac{14}{2}} \bigg[2(12)+(14-1)d\bigg]}\\\\\\\longrightarrow\rm{1078=7[24+13d]}\\\\\\\longrightarrow\rm{\cancel{\dfrac{1078}{7} }=24+13d}\\\\\\\longrightarrow\rm{154=24+13d}\\\\\\\longrightarrow\rm{13d=154-24}\\\\\\\longrightarrow\rm{13d=130}\\\\\\\longrightarrow\rm{d=\cancel{130/13}}\\\\\\\longrightarrow\bf{d=10}$

Now;

We know that formula of an A.P.;

$\boxed{\bf{a_n=a+(n-1)d}}}}$

• First term (a) = 10
• Common difference (d) = 10

$\longrightarrow\rm{a_{20}=10+(20-1)\times10}\\\\\longrightarrow\rm{a_{20}=10+19\times 10}\\\\\longrightarrow\rm{a_{20}=10+190}\\\\\longrightarrow\bf{a_{20}=200}$

Thus;

The 20th term will be 200 .