Question

The algebraic from of sum of an Arithmetic Sequence is n raised 2+ 2n.

a) Write the sequence.

b) What is the sum of first 10 terms ​

Answer 1

Step-by-step explanation:

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

As we know sum of n terms of an Arithmetic sequence is \frac{n}{2}[2 a+(n-1)d]

2

n

[2a+(n−1)d]

⇒n²+2 n=\frac{n}{2}[2 a+(n-1)d]

2

n

[2a+(n−1)d]

⇒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 S_{n}S

n

S_{n}S

n

= 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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Answer 2

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