Q) In a Geometric Progression (GP), the first term is 24 and the fifth term is 8. Find the ninth term of the GP.

ICSE Specimen Question paper (SQP) 2025

Ans:

Step 1: The geometric progression is a, a r, a r ², ar ³, ……… a r ^{n – 1}

here, a is the first term, r is the common ratio, n is n^th term.

Step 2: Given is the first term = 24

∴ a = 24 …………. (i)

Step 3: Next, given is the 5^th term is 8

∴ a₅ = 8

∴ a r ^{5 – 1} = 8

∴ a r ⁴ = 8 ……… (ii)

Step 4: From equation (i) in step 2, we have a = 24,

∴ (24) r ⁴ = 8

∴ r ⁴ =

∴ r ⁴ = ………. (iii)

Step 5: Next, We need to find the value of the 9^th term, a₉ 

∴ a₉  = a r ^{(9 – 1)}

∴ a₉  = a r ⁸  

∴ a₉  = a r ⁴ x r ⁴

Step 6: Now, we have a r ⁴ = 8  from equation (ii)

and r ⁴ = from equation (iii)

∴ a₉  = (8) x

∴ a₉  =

Therefore, the value of the ninth term in given GP is .

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