Math, asked by sanchithasanchitha71, 7 months ago

For what value of a, are (2a-1), 7 and 3a three consecutive terms of an A.P?​

Answers

Answered by wwwalison8888a
4

Step-by-step explanation:

if the terms are in ap it means

2b=a+b

7=(2a-1)+3a

7+1=5a

a=8/5

so terms are

11/5,7,24/5

Answered by Anonymous
14

Given:

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Three terms

  • First term = (2a-1)
  • Second Term = 7
  • Third Term = 3a

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To Find:

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Value of a for which the above three terms are in an AP

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Concept:

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For three terms to be in AP , the sum of first and third term should be equal to twice the second term.

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For three terms a , b and c to be in an AP:

2b = a + c

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Answer:

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From using the above concept, we get:

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2 * 7 = 2a - 1 + 3a

5a - 1 = 14

5a = 14 + 1

5a = 15

a = \dfrac{15}{5}

a = 3

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Therefore, the value of a is 3.

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First Term = 2*3 - 1 = 6 - 1 = 5

Second Term = 7

Third Term = 3*3 = 9

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Proof:

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Substituting the value of a in the terms, we get:

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First Term = (2*3 - 1) = 5

Second Term = 7

Third Term = 3*3 = 9

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2b = a + c

2*7 = 5 + 9

14 = 14

LHS = RHS

Hence Proved.

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Other AP Formulas:

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nth term of an AP

formulas

\\\\\sf 1) \: n_{th} \: term \: of \: any \: AP \: = a + (n - 1)d\\

\sf 2) \:n_{th} \: term \: from \: the \: end \: of \: an \: AP \: = a + (m - n)d\\

\sf 3) \:n_{th} \: term \: from \: the \: end \: of \: an \: AP = l - (n - 1)d\\

\sf 4) \: Difference \: of \: two \: terms = (m - n)d\\

where m and n is the position of the term in the AP

\sf 5) \:Middle\: term\: of\: a\: finite\: AP

\sf (i) \:\: If \: n \: is \: odd = \frac{n + 1}{2}\:th\:term

\sf (ii) \:\: If \: n \: is \: even = \frac{n}{2} \:th \: term \: and \: ( \frac{n}{2} + 1)th \: term\\

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Sum Formulas

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\sf 1) \: Sum \: of \: first \: n \: terms \: of \: an \:AP = \frac{n}{2} [ \: 2a + (n - 1)d \: ]\\

\sf 2) \: Sum \: of \: first \: n \: natural \: numbers = \frac{n(n + 1)}{2}\\

\sf 3) \: Sum \: of \: AP \: having \: last \: term = \frac{n}{2} [ \: a + l \: ]\\

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