The Algebraic form of sum of an Arithmetic Sequence is n2+2n (a) Write the Sequence (b) What is the sum of first 10 te

Question

The Algebraic form of sum of an Arithmetic Sequence is n2+2n

(a) Write the Sequence

(b) What is the sum of first 10 terms?​

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Raelynn 4 weeks 2021-09-21T23:50:37+00:00 1 Answer 0 views 0

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    2021-09-21T23:52:30+00:00

    Answer:

    Rule for the sum of arithmetic sequence=n²+2 n

    As we know sum of n terms of an Arithmetic sequence is

    ⇒n²+2 n=

    ⇒2(n+2)=2 a+ (n-1) d

    ⇒2 n + 4=2 a-d + n d

    Equating LHS and RHS

    ⇒2 n = n d and 2 a -d= 4

    ⇒ d=2 ∧ 2 a- 2=4

    ⇒2 a= 6

    ⇒a=3

    a). Sum of first 10 term of this sequence, put n=10 in

    = n²+ 2 n=10²+2×10=100+20=120

    (b) Let p terms are needed to get the sum 168.

    ⇒p²+ 2 p=168

    ⇒p²+ 2 p-168=0

    ⇒(p+14)(p-12)=0

    ⇒p≠ -14[ number of terms can’t be negative]

    So, p=12

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