17. The sum of the first five terms of an AP and the sum of first eleven terms of the same AP is 167.If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Answers
Answered by
2
S(n)=n/2(2a+(n-1)d)
S5+S11=167
S5 = 5/2(2a + 4d)
=5(a+2d)
S5= 5a + 10d ..............(1)
S11 = 11/2 (2a + 10d)
= 11 ( a + 5d)
S11= 11a + 55d ..............(2)
S5 + S11 = 167
So, (1)+(2)=167
ie; (5a+ 10d) + (11a+55d)=167
16a + 65d = 167.........(3)
S10=10a+45d=235.......(4)
Use elimination method for (3) and (4) to find the values of a and d respectively
Similar questions