Question

In an ap if 12th term is -13and the sum of 1st 4 terms is 24. What is the sum of the 1st 10 terms

Answer 1

Step-by-step explanation:

Given  

In an ap if 12th term is -13 and the sum of 1st 4 terms is 24. What is the sum of the 1st 10 terms

• Given t12 = - 13, S4 = 24.
• We know that tn = a + (n – 1)d
•                                          -13 = a + (12 – 1)d
•                                So a + 11d = - 13
• We know that Sn = n/2 (2a + (n – 1)d)
•                        24 = 4/2 (2a + (4 – 1) d)
•                        24 = 2(2a + 3d)
•                             2a + 3d = 12
•   Now   a + 11d = - 13
•             2a + 3d = 12
• Multiply eqn 1 by 2 we get
•           2a + 22d = - 26
•           2a + 3d  = 12
•                   19d = - 38
•              So d = - 2
• Also 2a – 6 = 12
•          2a = 18
•       So a = 9
• Now for sum of 10 terms we have a = 9, d = - 2 and n = 10
• Sn = n/2 (2a + (n – 1)d)
•     = 10/2 (2(9) + (10 – 1) (-2)
•    = 5(18 – 18)
•   = 0

Therefore sum of 10 terms is zero

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