Question

The sum of first 20 terms in an ap is 210.find sumof 10th and 11th term

Answer 1

As per question, sum of first 20 terms in an AP is 210.So, we can write as below:$S_{n} = \frac{n}{2}(2a+(n-1)d)$
where, $S_{n}$ = sum of n terms
a = first term of AP
d = common difference
n = no of terms
=> $S_{20} = \frac{20}{2}(2a+(20-1)d)$
=> 210 = 10(2a+ 19d)  
=> 21 = 2a+19d -----  $eq^{n}$(i)

Since, $t_{n}$= a+(n-1)d
where $t_{n}$= nth term of an AP
So, $t_{10}$= a+ (10-1)d = a+ 9d   
      $t_{11}$= a+ (11-1)d = a+ 10d
      $t_{10}$+$t_{11}$= 2a+ 19d  --- $eq^{n}$(ii)

Substituting $eq^{n}$(i) in $eq^{n}$(ii)=> $t_{10}$+$t_{11}$= 21
Hence, sum of 10th and 11th term is 21.