The sum of first five terms in AP is 55and sum of first 10 terms in AP is 235.find the sum of first 20 terms. 

Asked by kolatejayashree | 17th May, 2020, 08:02: PM

Expert Answer:

Let 'a' and 'd' be the first term and common difference of an A.P. respectively.
Sum of first five terms is 55 i.e. Sn = n/2[2a+(n-2)d]
S5 = 5/2[2a+(5-1)d]
55 = 5/2[2a+4d]
a+2d=11 ... (i)
 
Sum of first 10 terms is 235 i.e. Sn = n/2[2a+(n-2)d]
S10 = 10/2[2a+(10-1)d]
235 = 5[2a+9d]
2a+9d=47 ... (ii)
 
Multiplying (i) by 2, we get
2a+4d=22 ... (iii)
2a+9d=47 ... (ii)
Subtracting (ii) from (iii), we get
-5d=-25
d=5
Substituting in (i), we get
a+2(5)=11
a=1
Sum of first 20 terms is S20 = 20/2[2(1)+(20-1)5] = 10[2+95] = 10(97) = 970

Answered by Renu Varma | 17th May, 2020, 08:37: PM