CBSE Class 10 Answered
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 | 17 May, 2020, 20:02: PM
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 | 17 May, 2020, 20:37: PM
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