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If the sum of 4^ th and 7^ th term of an AP is 31 and sum of first two term is 7 then find the 10^ th term of A P is

Options

  1. A20
  2. B29
  3. C33
  4. D28

Correct answer

B. 29

Step-by-step solution

Let a be the first term and d is the common difference also a_n be the n^ th term. array ll & a₄+a₇=31 & a+3 d+a+6 d=31 [ a_n=a+(n-1) d ] & 2 a+9 d=31 ...(i) & a₁+a₂=7 & a+a+d=7 & 2 a+d=7 .....(ii) array Subtract Eq. (ii) from Eq. (i), we get aligned & 2 a+9 d-2 a-d=31-7 & 8 d=24 & d=3 & 2 a+3=7 & a=2 & a₁₀=a+9 d & =2+27=29 aligned

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