Home
Class 10
MATHS
If a(n)=(n^(2))/(3n+2), find a(1)a(5)....

If `a_(n)=(n^(2))/(3n+2)`, find `a_(1)a_(5)`.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the values of \( a_1 \) and \( a_5 \) using the given formula \( a_n = \frac{n^2}{3n + 2} \), and then calculate \( a_1 \times a_5 \). ### Step-by-Step Solution: 1. **Find \( a_1 \)**: - Substitute \( n = 1 \) into the formula: \[ a_1 = \frac{1^2}{3(1) + 2} \] - Calculate the numerator and denominator: \[ a_1 = \frac{1}{3 + 2} = \frac{1}{5} \] 2. **Find \( a_5 \)**: - Substitute \( n = 5 \) into the formula: \[ a_5 = \frac{5^2}{3(5) + 2} \] - Calculate the numerator and denominator: \[ a_5 = \frac{25}{15 + 2} = \frac{25}{17} \] 3. **Calculate \( a_1 \times a_5 \)**: - Multiply the two values obtained: \[ a_1 \times a_5 = \left(\frac{1}{5}\right) \times \left(\frac{25}{17}\right) \] - Simplify the multiplication: \[ a_1 \times a_5 = \frac{1 \times 25}{5 \times 17} = \frac{25}{85} \] - Further simplify: \[ a_1 \times a_5 = \frac{5}{17} \] ### Final Answer: \[ a_1 \times a_5 = \frac{5}{17} \]
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSION (A.P.)

    MCGROW HILL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|15 Videos

  • ANALYTICAL REASONING

    MCGROW HILL PUBLICATION|Exercise EXERCISE|24 Videos

  • ARITHMETICAL REASONING TEST

    MCGROW HILL PUBLICATION|Exercise EXERCISE|25 Videos

Similar Questions

Explore conceptually related problems

If n^(th) terms of the sequence {a_(n)} where a_(n)=(-1)^(n-1)5^(n+1) , find a_(1),a_(2) , and a_(3) is

The Fibonacci sequence is defined by 1=a_(1)=a_(2) and a_(n)=a_(n-1)+a_(n-2),n>2 Find (a_(n+1))/(a_(n)),f or n=5

The Fibonacci sequence is defined by 1=a_(1)=a_(2) and a_(n)=a_(n-1)+a_(n-2),n>2 Find (a_(n+1))/(a_(n)) for n=1,2,3,4,5

If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in

Find the indicated terms in each of the following sequences whose n^(th) terms are a_(n) = (a_(n-1))/(n^(2)) , (n ge 2) , a_(1) =3 , a_(2) , a_(3)

Find the first five terms of the following sequences and write down the corresponding series (i) a_(n) = (1)/(5) (2n -3) (ii) a_(1) =a_(2) = 1 , a_(n) = a_(n-1) + a_(n-2) , n gt 2

A sequence is defined as follows : a_(a)=4, a_(n)=2a_(n-1)+1, ngt2 , find (a_(n+1))/(a_(n)) for n=1, 2, 3.

Find the indicated terms in each of the following sequences whose nth terms are: a_(n)=5_(n)-4;a_(12) and a_(15)a_(n)=(3n-2)/(4n+5);a+7 and a_(8)a_(n)=n(n-1);a_(5)anda_(8)a_(n)=(n-1)(2-n)3+n);a_(1),a_(2),a_(3)a_(n)=(-1)^(n)n;a_(3),a_(5),a_(8)

Find the term indicated in each case: (i) a_(n)=(n^(2))/(2^(n)):a_(7) (ii) a_(n)=(n(n-2))/(n-3),a_(20) (iii) a_(n)=[(1+(-1)^(n))/2 3^(n)],a_(7)