Math, asked by priyanshurathod0, 4 months ago

find the sum of n term of the series 2.5 + 5.8 + 8.11 +...​

Answers

Answered by llHeartHackerll
1

Answer:

HEY !! HERE IS YOUR REQUIRED ANSWER STEPWISE-:

The First sequence in the series is 2+5+8+…n terms

This is an A.P. with first term as 2 and common difference 3.

∴T¹ =2+3(n−1)=3n−1

The Second sequence in the series is 5+8+11…n terms

This is an A.P. with first term as 5 and common difference 3

∴T² =5+3(n−1)=3n+2

Thus n term of the series =(3n−1) (3n+2) = 9n² + 3n - 2

Therefore, Sn = ∑(9n² + 3n - 2 =

 \frac{9n(n + 1)2n + 1}{6}  +  \frac{3n(n + 1)}{2}  - 2n

= 3n² ( n + 1 )

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