Math, asked by ashly531265, 11 months ago

find the 13th term of an arithmetic sequence if five times the fifth term is equal to the 8 times the 8th term​

Answers

Answered by simranrawal
4

Answer:

0

Step-by-step explanation:

If a×a th term=b×b th term

Than (a+b) th term=0

Therefore (5+8) th term =0

13 th term=0

Alternative method

Attachments:
Answered by TRISHNADEVI
6

 \huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \:   \: QUESTION \:  \: } \mid}}}}}

 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \text{ Find the 13th term of an arithmetic sequence,} \\ \text{if 5 times the 5th term of an AP is equal to 8 times  } \\  \text{ its 8th term.}</p><p>

 \huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \:   \: SOLUTION \:  \: } \mid}}}}}

 \underline{ \mathfrak{  \:  \: Given, \:  \: }} \\\  \\  \mathtt{ \rightsquigarrow  5 \:  times \:  \:  of  \:  \: the  \:  \: 5th  \:  \: term = 8th \:  \:times} \\ \mathtt{ \: \: \: \:  \:\: \: \: \: \:\: \: \: \: \: \:\: \: \: \: \: \: \: \: \:\: \: \:\: \: \:\: \:  \: \: of  \:  \: the  \:  \: 8th  \:  \: term} \\  \\  \\  \underline{ \mathfrak{ \:  \: </p><p>To  \: find : \mapsto \:  \: }} \\  \\  \mathtt{ \rightsquigarrow \: 13th  \:  \: term \:  \:  of \:  \:  the \: \: A.P. }

 \underline{ \mathfrak{ \:  \: Suppose, \:  \: }} \\   \\ \mathtt{ \rightsquigarrow \: First  \:  \: term  \:  \: of  \:  \: the  \:  \: A.P. = a} \\  \mathtt{ \rightsquigarrow \: Difference = d}

 \underline{ \bold{ \:  A.T.Q.,  \: }} \\  \\ \:  \:  \:  \:  \:  \:  \mathtt{ 5  \times T_5 = 8 \times  T_8 }\\  \\ \mathtt{\Longrightarrow \:  5[ a + (5-1)d]=8 [ a + (8-1)d]} \\  \\   \mathtt{\Longrightarrow 5(a  + 4d)= 8 (a+7d) }\\  \\    \mathtt{ \Longrightarrow 5a + 20 \: d = 8a + 56 \: d} \\  \\  \mathtt{  \Longrightarrow 5a - 8a = 56 \: d    - 20 \: d}\\  \\  \mathtt{\Longrightarrow - 3a   =  36 \: d}\\  \\   \mathtt{\Longrightarrow  a =  \frac{36 \: d}{ -  3}}  \\  \\  \:  \:  \:  \mathtt{ \therefore \:  \: \underline{  \: a = -  12 \: d \: }}

  \underline{\mathfrak{ \: Now \: }} \\  \\ \mathtt {13th  \:  \: term,  \: T_{13 }= a + [(13-1)d] } \\  \\    \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \mathtt{ = a + 12 \: d} \\  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \mathtt{ = ( - 12 \: d) + 12 \: d } \\  \mathtt{\:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:   \red{[As \:  \: a  =  - 12 \: d]}} \\  \\    \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\mathtt{ =  - 12 \: d + 12 \: d} \\  \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  \:  \:  \:  \:  \:  \: \:  \mathtt{ = 0} \\  \\  \\    \huge{\mathtt{ \therefore \:  \:  \underline{ \:  \: 13th  \:  \: term \:  = 0 \:  \: }} }

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