2011

Mathematics

JAMB

The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms

A.

60

B.

62

C.

54

D.

64 Correct Answer: 62

Explanation

T₂ = 4, T₄ = 16 T_x = ar^n-1 T₂ = ar2-1 = 4 i.e. ar³ = 16, i.e. ar = 4 T₄ = ar^4-1 therefore, T₄ /T_r = ar³/ar = 16/4 r² = 4 and r = 2 but ar = 4 a = 4/r = 4/2 a = 2 Sⁿ = a(rⁿ−1)/r−1 S⁵ = 2(2⁵−1)/2−1 = 2(32−1)/2−1 = 2(31) = 62

T₂ = 4, T₄ = 16 T_x = ar^n-1 T₂ = ar2-1 = 4 i.e. ar³ = 16, i.e. ar = 4 T₄ = ar^4-1 therefore, T₄ /T_r = ar³/ar = 16/4 r² = 4 and r = 2 but ar = 4 a = 4/r = 4/2 a = 2 Sⁿ = a(rⁿ−1)/r−1 S⁵ = 2(2⁵−1)/2−1 = 2(32−1)/2−1 = 2(31) = 62

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2011

Mathematics

JAMB

The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms

A.

60

B.

62

C.

54

D.

64

Correct Answer: 62

Explanation

T2 = 4, T4 = 16 Tx = arn-1 T2 = ar2-1 = 4 i.e. ar3 = 16, i.e. ar = 4 T4 = ar4-1 therefore, T4 /Tr = ar3/ar = 16/4 r2 = 4 and r = 2 but ar = 4 a = 4/r = 4/2 a = 2 Sn = a(rn−1)/r−1 S5 = 2(25−1)/2−1 = 2(32−1)/2−1 = 2(31) = 62

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T₂ = 4, T₄ = 16 T_x = ar^n-1 T₂ = ar2-1 = 4 i.e. ar³ = 16, i.e. ar = 4 T₄ = ar^4-1 therefore, T₄ /T_r = ar³/ar = 16/4 r² = 4 and r = 2 but ar = 4 a = 4/r = 4/2 a = 2 Sⁿ = a(rⁿ−1)/r−1 S⁵ = 2(2⁵−1)/2−1 = 2(32−1)/2−1 = 2(31) = 62