If a_12=5a_4−8 and a_4=17 in an AP, what is a_20?
Answer and explanation
Correct answer: 137
Use the arithmetic-progression relation a_n=a_k+(n−k)d. First evaluate the twelfth term from the given condition: a_12=5a_4−8=5(17)−8=85−8=77. Therefore a_12−a_4=77−17=60. The index gap from the fourth term to the twelfth term is 8, so 8d=60 and d=7.5. From a_4 to a_20 there are 20−4=16 equal steps. Hence a_20=a_4+16d=17+16(7.5)=17+120=137. Thus option A is correct. The other values would require a different common difference and would not preserve the relation between the fourth and twelfth terms. A fractional common difference is acceptable in an AP.
Frequently asked questions
What is the correct answer to this question?
137
Why is this the correct answer?
Use the arithmetic-progression relation a_n=a_k+(n−k)d. First evaluate the twelfth term from the given condition: a_12=5a_4−8=5(17)−8=85−8=77. Therefore a_12−a_4=77−17=60. The index gap from the fourth term to the twelfth term is 8, so 8d=60 and d=7.5. From a_4 to a_20 there are 20−4=16 equal steps. Hence a_20=a_4+16d=17+16(7.5)=17+120=137. Thus option A is correct. The other values would require a different common difference and would not preserve the relation between the fourth and twelfth terms. A fractional common difference is acceptable in an AP.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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