Maths · Arithmetic and Geometric progressions

The sum of the first tern and the fifth term of an ascending A.P. is 26 and the

The sum of the first tern and the fifth term of an ascending A.P. is 26 and the product. of the second term by the fourth term is \( 160 . \) And the sum of the first seven terms of this AP.

  • A. 110
  • B. 114
  • C. 112
  • D. 116

Step-by-step solution

Let the AP be a, a+d, a+2d, a+3d, a+4d,... Given: a + (a+4d)=26 → 2a+4d=26 → a+2d=13 → a=13-2d. Also (a+d)(a+3d)=160 → (13-d)(13+d)=169-d²=160 → d²=9 → d=3 (positive). Then a=13-6=7. Sum of first 7 terms = (7/2)(2a+6d) = (7/2)(14+18)= (7/2)*32=112.
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