1.

The sum of first q terms of an AP is 162.ration of its 6th term and 15th term is 1:2 respectively. Find first term and 15 term. In numbers

Answer»

It think the question might be 9 terms instead of q terms. if it is q terms then we would not get the values of the terms in numbers.Here is the solution of the problem if the sum of 9 terms of A.P is 162.Given,

Sum of terms= 162Ratio of 6th term and 13th term= 1:2Formula is an= a₁+(n-1)d

Then the sixth term a₆= a₁+5dThe 13th term is a₁₃=a₁+12dAs given a6/a₁₃ is 1/2(a₁+5d)/(a₁+12d)=1/2

After cross multiplication2(a₁+5d)=1(a₁+12d)2a₁+10d=a1+12d2a₁-a₁=12d-10dTherefore the first term a₁=2dSn=(n/2)[2a+(n-1)d]S₉=(9/2)[2(2d)+(9-1)d]S₉=(9/2)(4d+8d)162=(9/2)(12d)162=9(6d)54d=162d=3a1=2d=2(3)=6a₁₅=6+(15-1)3=6+3(14)=48The first term of A.P is 6The 15th term of A.P is 48

9 hota to may solve nahi kar leta


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