Question

If the first term of an arithmetic sequence is 10 and sum of first term and 21st term is 140 what is its 11th term

Answer 1

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

$\tt{\implies first\: term\:(a)=10}$

$\rm{\implies Sum\:_{(1th+21th\: terms)}=140}$

$\sf\large\underline{To\: Find:}$

$\tt{\implies 11th\:term\:of\:AP=?}$

$\sf\large\underline{Solution:}$

• by applying formula to calculate d than putting the value of a and d to find out the value of 11th term]

$\tt{\implies Sum\:_{(1st+21th\:terms)}=140}$

$\tt{\implies 10+(1-1)d+10+(21-1)d=140}$

$\tt{\implies 20+20d=140}$

$\tt{\implies 20d=140-20}$

$\tt{\implies d=6}$

• Now calculate 11th term here]

$\tt{\implies T\:_{(n)}=a+(n-1)d}$

$\tt{\implies T\:_{(11)}=10+(11-1)\times6}$

$\tt{\implies T\:_{(11)}=10+60}$

$\tt{\implies T\:_{(11)}=70}$

$\sf\large{Hence,}$

$\bf{\implies 11th\:term\:of\:AP=70}$