Question 32 of 51beginner🔧 ApplyNumerical3 marks

Find the 10th10^{th} and nthn^{th} terms of the GP: 5, 25, 125, ….

Correct Answer

(10th term) 5105^{10}

(nth term) 5n5^{n}

Exercise: Exercise Set 8.3 | Q: 2 | (Page 20)
For More Understanding

Explanation

To find the terms of a geometric progression, we first identify the first term and the common ratio. The nth term formula for a GP is then applied with these values to get a general expression, which is subsequently used to find specific terms like the 10th term.

Solution Steps

  1. Step 1: Identify the first term (aa) and common ratio (rr) of the given GP: 5, 25, 125, … . Here, a=5a = 5 and r=25/5=5r = 25 / 5 = 5.

  2. Step 2: Recall the formula for the nthn^{th} term of a GP: tn=arn−1t_n = ar^{n-1}.

  3. Step 3: Substitute a=5a = 5 and r=5r = 5 into the formula to find the nthn^{th} term: tn=5×5n−1=5nt_n = 5 \times 5^{n-1} = 5^n.

  4. Step 4: Substitute n=10n = 10 into the nthn^{th} term formula to find the 10th10^{th} term: t10=5×510−1=5×59=510t_{10} = 5 \times 5^{10-1} = 5 \times 5^9 = 5^{10}.

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