Exams Joint Entrance Examination Mathematics Sequences and Series Question 61 Question 61 of 519 Medium MCQ
Let 2 , 8 {2}^{},{8}^{} 2 , 8 and 44 {44}^{} 44 terms of a non-constant A. P. be respectively the 1 , 2 {1}^{},{2}^{} 1 , 2 and 3 {3}^{} 3 terms of a G. P. If the first term of the A. P. is 1, then the sum of its first 20 terms is equal to -
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1 + d , 1 + 7 d , 1 + 43 d ( 1 + 7 d ) 2 = ( 1 + d ) ( 1 + 43 d ) 1 + 49 d 2 + 14 d = 1 + 44 d + 43 d 2 6 d 2 − 30 d = 0 d = 5 S 20 = 20 2 [ 2 × 1 + ( 20 − 1 ) × 5 ] = 10 [ 2 + 95 ] = 970 \begin{gathered} 1+d,\, 1+7d,1+43d \\ (1+7d{)}^{2}=(1+d)(1+43d) \\ 1+49{d}^{2}+14d=1+44d+43{d}^{2} \\ 6{d}^{2}-30d=0 \\ d=5 \\ {S}_{20}=\frac{20}{2}[2\times 1+(20-1)\times 5] \\ \, =10[2+95] \\ \, =970 \end{gathered} 1 + d , 1 + 7 d , 1 + 43 d ( 1 + 7 d ) 2 = ( 1 + d ) ( 1 + 43 d ) 1 + 49 d 2 + 14 d = 1 + 44 d + 43 d 2 6 d 2 − 30 d = 0 d = 5 S 20 = 2 20 [ 2 × 1 + ( 20 − 1 ) × 5 ] = 10 [ 2 + 95 ] = 970 Answer the question to unlock