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The sum of first q term of an AP is 162 .the ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of an AP
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The sum of first q term of an AP is 162 .the ratio of its 6th term to ...
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there is a mistake 9 will be come not q..
Given,
Sum of 9 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........ (1)
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's help
there is a mistake 9 will be come not q..
Given,
Sum of 9 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........ (1)
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's help
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The sum of first q term of an AP is 162 .the ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of an AP?
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The sum of first q term of an AP is 162 .the ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of an AP? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The sum of first q term of an AP is 162 .the ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of an AP? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of first q term of an AP is 162 .the ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of an AP?.
The sum of first q term of an AP is 162 .the ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of an AP? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The sum of first q term of an AP is 162 .the ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of an AP? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of first q term of an AP is 162 .the ratio of its 6th term to its 13th term is 1:2. Find the first and 15th term of an AP?.
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