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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