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In an AP, the sum of …

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In an AP, the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP

    • Posted by Rashmitha Bangera989 6 years, 2 months ago

    CBSE > Class 10 > Mathematics
    • 3 answers

    Dhruv Kakkar 6 years, 2 months ago

    Given: Sum of first ten terms of an AP = -150 Sum of next ten terms of an AP =-550 To find: AP Solution: Sum of n terms of an AP Sum of first 10 terms -150 = 5(2a+9d) -150=10a+45d…..(i) Sum of next 10 terms -150-550=10(2a+19d) -700=10(2a+19d) -70=2a+19d …….(ii) Combining 1 and 2, we get Multiplying (ii) by 5 -350=10a+95d….(iii) Subtracting (i) from (iii) we get, -350+150=10a+95d-10a-45d -200=50d d=-4 substitute d=-4 in equation (i) we get -150=10a+45d -150=10a+45(-4) -150=10a-180 10a=-150+180 10a=30 a=3 hence, a=3 and d=-4 The AP will be a, a+d, a+2d, a+3d,… Then the AP will be 3, -1, -5, -9,…."

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    Dhruv Kakkar 6 years, 2 months ago

    Given: Sum of first ten terms of an AP = -150 Sum of next ten terms of an AP =-550 To find: AP Solution: Sum of n terms of an AP Sum of first 10 terms -150 = 5(2a+9d) -150=10a+45d…..(i) Sum of next 10 terms -150-550=10(2a+19d) -700=10(2a+19d) -70=2a+19d …….(ii) Combining 1 and 2, we get Multiplying (ii) by 5 -350=10a+95d….(iii) Subtracting (i) from (iii) we get, -350+150=10a+95d-10a-45d -200=50d d=-4 substitute d=-4 in equation (i) we get -150=10a+45d -150=10a+45(-4) -150=10a-180 10a=-150+180 10a=30 a=3 hence, a=3 and d=-4 The AP will be a, a+d, a+2d, a+3d,… Then the AP will be 3, -1, -5, -9,…."

    0Thank You

    Pratik Kaushal 6 years, 2 months ago

    So .. Given that Sum of first 10 terms is -150 and of next 10 is -550 so S10 =-150 -150 = 10/2(2a+(10-1)d =2a+9d = -30 .....(1) And again given that sum of next ten terms is -550 So -150 +(-550) =-770 -770= 20/2(2a+(20-1)d) =2a+19d=-70......(2) By applying elimination b/w both We get 10d = -40 d= -4... Putting d=-4 in eq 1.... 2a+9(-4) = -30 2a-36 =-30 2a = 6 a = 3 So Ap would be .... 3 , -1,-5,-9,..... Hope it will help you :)..... Have a nice day !!

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