If the common difference of an ap is 3 then a20 – a15 is

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If the common difference of an ap is 3 then a20 – a15 is

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Raelynn 1 week 2021-09-14T18:32:16+00:00 2 Answers 0 views 0

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    0
    2021-09-14T18:33:16+00:00

    GIVEN :

    • Common difference (d) = 3

    TO FIND :

     \bf  a_{20} - a_{15} = ?

    SOLUTION :

    • We know that nth term of A.P. if first term is ‘a’ –

     \bf \implies \large{ \boxed{ \bf a_{n} = a + (n - 1)d }}

    • Now –

     \bf \implies a_{20} = a + (20 - 1)d

     \bf \implies a_{20} = a +19d

    • And –

     \bf \implies a_{15} = a + (15 - 1)d

     \bf \implies a_{15} = a +14d

    • So that –

     \bf \implies a_{20} - a_{15} =(a +19d) - (a + 14d)

     \bf \implies a_{20} - a_{15} = 19d-  14d

     \bf \implies a_{20} - a_{15} = 5d

     \bf \implies a_{20} - a_{15} = 5(3)

     \bf \implies \large{ \boxed{ \bf a_{20} - a_{15} = 15}}

    0
    2021-09-14T18:34:08+00:00

    Answer:

    We know that,

    an=a+(n-1)d

    So,a20=a+(20-1)(3)

    a20=a+19(3)

    a20=a+57

    Similarly, a15=a+14d

    a15=a+14(3)

    a15=a+42

    Now,a20-a15=(a+57)-(a+42)

    =a+57-a-42

    =57-42

    =15

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