If-a-1-1-and-a-1-a-2-a-n-n-2-Find-a-2-a-13-

Question Number 202303 by hardmath last updated on 24/Dec/23

If a_{1} = 1 and a_{1} \cdot a_{2} \cdot \dots \cdot a_{n} = n^{2}

Find : a_{2} + a_{13} = ?

Answered by MATHEMATICSAM last updated on 24/Dec/23

a_{1} \cdot a_{2} \cdot \dots . \cdot a_{n} = n^{2}

∴ a_{1} \times a_{2} \times a_{3} \times \dots . \times a_{13} = 13^{2} = 169

\Rightarrow a_{13} = \frac{169}{a_{1} \times a_{2} \times a_{3} \times \dots . . \times a_{12}} = \frac{169}{144}

a_{1} \times a_{2} = 2^{2} = 4

\Rightarrow a_{2} = 4 [∵ a_{1} = 1]

a_{2} + a_{13} = 4 + \frac{169}{144} = \frac{745}{144}

Commented by hardmath last updated on 24/Dec/23

thankyou dear ser

Answered by mr W last updated on 24/Dec/23

a_{1} a_{2} \dots a_{n - 1} a_{n} = n^{2}

a_{1} a_{2} \dots a_{n - 1} = {(n - 1)}^{2}

\Rightarrow a_{n} = {(\frac{n}{n - 1})}^{2}

a_{2} + a_{13} = {(\frac{2}{1})}^{2} + {(\frac{13}{12})}^{2} = \frac{745}{144}

Commented by hardmath last updated on 24/Dec/23

thankyou dear professor cool

Answered by 1990mbodji last updated on 24/Dec/23

O n s u p p o s e q u e a_{1} = 1 e t a_{1} . a_{2} \dots a_{n} = n^{2} .

T r o u v o n s l a v a l e u r d e a_{2} + a_{13} .

a_{1} a_{2} = 4 \Rightarrow a_{2} = 4

a_{1} a_{2} a_{3} = 9 \Rightarrow a_{3} = \frac{9}{4}

P a r i t \overset{´}{e r a t i o n} : a_{13} = \frac{169}{144}

D o n c a_{2} + a_{13} = 4 + \frac{169}{144} \Rightarrow a_{2} + a_{13} = \frac{745}{144}

Commented by hardmath last updated on 24/Dec/23

thankyou dear ser