The sum of the first five terms of an arithmetic sequence is 150 and the sum of the first ten terms is 550. (b) What is the eighth ter

Question

The sum of the first five terms of an arithmetic sequence is 150 and the sum of the first ten terms is 550.
(b) What is the eighth term?

in progress 0
Delilah 2 days 2021-10-11T13:07:31+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-11T13:08:41+00:00

     Let \: 'a' \: and \: 'd'\: are \: first \: term \: and

     common \: difference \: of \: an \: A.P

     \pink {Sum \: of \: first \: n \: terms}

     \pink { = \frac{n}{2} [ first \: term + last \:term ]}

    i ) Sum \: of \: first \: five \: terms = 150

     \implies \frac{5}{2}[ a + a + 4d ]= 150

     \implies \frac{5}{2}[ 2a+ 4d ] = 150

     \implies 2a+ 4d  = 150 \times \frac{2}{5}

     \implies 2a + 4d = 60 \: --(1)

    ii) Sum \: of \: first \: ten \: terms = 550

     \implies \frac{10}{2}[ a + a + 9d ]= 550

     \implies 5[ 2a+ 9d ]= 550

     \implies 2a+ 9d  =  \frac{550}{5}

     \implies 2a + 9d = 110 \: --(2)

    /* Subtract equation (1) from Equation (2) , we get*/

     \implies 5d = 50

     \implies d = \frac{50}{5}

     \implies d = 10

    /* Put d = 10 in equation (1) , we get */

     2a + 4 \times 10 = 60

     \implies 2a + 40 = 60

     \implies 2a  = 60 - 40

     \implies 2a  = 20

     \implies a  = \frac{20}{2}

     \implies a  = 10

    /* We know that , */

     \boxed{ \blue { n^{th} \:term (a_{n}) = a+(n-1)d }}

     Eighth \:term = a + (8-1)d

     = a + 7d

     = 10 + 7 \times 10

     = 10 + 70

     = 80

    Therefore.,

     \red{ Eighth \:term\: of \: an \: A.P : } \green { = 80 }

    •••♪

    0
    2021-10-11T13:09:09+00:00

    sum of first five terms of AP = 150

    sum of first ten terms of AP = 550

Leave an answer

Browse

14:4+1-6*5-7*14:3+5 = ? ( )