Find the sum of given arithmetic progression 8 + 11 + 14 + 17 upto 15 terms

Shortcut Trick

Formula Used:

Average = (Sum of observations)/(Number of observations)

Last term = a + (n - 1)d

Calculation: 

The above series is in arithmetic progression so the middlemost term 8th term will be the average

⇒ 8^th term = 8 + (8 - 1) × 3 = 29

⇒ Sum of the series = 29 × 15 = 435

∴ The sum of the above series is 435  

Additional Information

We can avoid this above (29 × 15) multiplication by digit sum Method and option

The digit sum of 29 is  (2 + 9) ⇒ (11) ⇒ (2) and 15 is (1 + 5) = 6 

⇒ 2 × 6 = 12 ⇒ (1 + 2) ⇒ 3 

Now check the options whose digit sum will be 3 there is only option 2 whose Digit sum is 3 

∴ 435 is the right answer

Traditional Method: 

Given:

Arithmetic progression 8 + 11 + 14 + 17 upto 15 terms

Formula Used: 

Sum of arithmetic progression = n[2a + (n - 1)d]/2

Calculation:

Sum of 1st 15 terms = 15[2 × 8 + (15-1)3]/2

⇒ (15 × 58)/2

⇒ 435

∴ 435 is the right answer