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The sum of first 24 terms of an A.P. a1, a2, a3,...; if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225, is equal to :
  • a)
    90
  • b)
    180
  • c)
    900
  • d)
    1800
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The sum of first 24 terms of an A.P. a1, a2, a3,...; if it is known th...
a1 + a5 + a10 +a15 + a20 + a24  = 225        (given)

(a1+a24) + (a5+a20) + (a10+a15) = 225            ...1

let first term is a & common difference is d then

 a1 = a       ,  a24 = a+23d   ,       a1+a24 = 2a+23d            ....2

 

 a5 = a+4d ,  a20 = a+19d ,         a5+a20 = 2a+23d           ....3

 

 a10 = a+9d , a15 = a+14d ,        a10+a15 = 2a+23d          ....4

putting 2 , 3 , 4 in eq 1 we get

3(2a+23d) = 225

 2a+23d = 75             ....5

now , a1 + a2 + a3 ....a24 = S24

   S24 = 24/2[2a+(24-10d)]

          =12(2a+23d)             ....6

from 5 & 6

S24 = 12*75 = 900
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The sum of first 24 terms of an A.P. a1, a2, a3,...; if it is known that a1+ a5+ a10+ a15+ a20+ a24=225, is equal to :a)90b)180c)900d)1800Correct answer is option 'C'. Can you explain this answer?
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The sum of first 24 terms of an A.P. a1, a2, a3,...; if it is known that a1+ a5+ a10+ a15+ a20+ a24=225, is equal to :a)90b)180c)900d)1800Correct answer is option 'C'. Can you explain this answer? 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 24 terms of an A.P. a1, a2, a3,...; if it is known that a1+ a5+ a10+ a15+ a20+ a24=225, is equal to :a)90b)180c)900d)1800Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of first 24 terms of an A.P. a1, a2, a3,...; if it is known that a1+ a5+ a10+ a15+ a20+ a24=225, is equal to :a)90b)180c)900d)1800Correct answer is option 'C'. Can you explain this answer?.
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