Question

Question 8 Find the sum to n terms in the geometric progression 7^0.5, 21^0.5, 3*7^0.5,...

Class X1 - Maths -Sequences and Series Page 192

Answer 1

√7, √21, 3√7, .......... n terms
√7 , √(7×3) , √(7 × 3²), ....... n terms
√7, √3 × √7 , (√3)² × √7 .......... n terms
here,
first term (a) = √7
common ratio ( r) = √3 × √7/√7 = √3
now use the formula ,
S_n = a(rⁿ -1)/(r -1)
= √7(√3ⁿ -1)/(√3 -1)
= √7{3^(n/2) - 1}(√3 + 1)/(√3 -1)(√3 + 1)
= √7{3^(n/2) -1}(√3 + 1)/(√3²-1²)
= [√7{3^(n/2) -1}(√3+1)]/2