Question

the sum of first q terms of an ap is 162 the ratio of its 6 to its 13 term is 1: 2. Find the first and 15 term of ap. Plz solve it fast.

Answer 1

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= 162

Ratio of 6th term and 13th term= 1:2

Formula is an= a1+(n-1)d

Then the sixth term a6= a1+5d

The 13th term is a13=a1+12d

As given a6/a13 is 1/2

(a1+5d)/(a1+12d)=1/2

After cross multiplication

2(a1+5d)=1(a1+12d)

2a1+10d=a1+12d

2a1-a1=12d-10d

Therefore the first term a1=2d

Sn=(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=162

d=3

a1=2d=2(3)=6

a15=6+(15-1)3=6+3(14)=48

The first term of A.P is 6

The 15th term of A.P is 48

HOPE IT HELPS YOU.

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