Question

the sum of first 5 terms and first 15 term of an ap are equal. find the sum of its first 20 terms​

Answer 1

Step-by-step explanation:

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

Answer 2

Step-by-step explanation:

please see the attachment