How i solve the question of arithmetic progressions of exercise 5.3 of class 10th of math in easy way. Because it is very important for board exam Find the sum of the following APs.(ii) − 37, − 33, − 29 ,…, to 12 terms

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# Find the sum of the following APs.(ii) − 37, − 33, − 29 ,…, to 12 terms Q.1(2)

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Given, −37, −33, −29 ,…, to 12 terms

For this A.P.,

first term, a = −37

And common difference, d = a

_{2}− a_{1}d= (−33)−(−37)

= − 33 + 37 = 4

n = 12

We know that, the formula for sum of nth term in AP series is,

S

_{n}= n/2 [2a+(n-1)d]S

_{12}= 12/2 [2(-37)+(12-1)×4]= 6[-74+11×4]

= 6[-74+44]

= 6(-30) = -180