# SAT math: SUMS (elite formulas)

## 26 terms

### n(n+1)/2

sum of first n consecutive integers

### 4(4+1)/2= 10

sum of first 4 consecutive integers

### 5(5+1)/2= 15

sum of first 5 consecutive integers

### 20(20+1)/2= 210

sum of first 20 consecutive integers

### 8(8+1)/2= 36

sum of first 8 consecutive integers

### 30(30+1)/2= 465

sum of first 30 consecutive integers

### n^2

sum of first n odd integers

### 5^2= 25

sum of first 5 odd integers

### 6^2= 36

sum of first 6 odd integers

### 11^2= 121

sum of first 11 odd integers

### 15^2= 225

sum of first 15 odd integers

### n(n+1)(2n+1)/6

sum of consecutive squares

### 3(3+1)(3*2+1)/6= 14

sum of consecutive squares up to 3^2

### 4(4+1)(4*2+1)/6= 30

sum of consecutive squares up to 4^2

### 5(5+1)(5*2+1)/6= 55

sum of consecutive squares up to 5^2

### 6(6+1)(6*2+1)/6= 91

sum of consecutive squares up to 6^2

### 7(7+1)(7*2+1)/6= 140

sum of consecutive squares up to 7^2

### 20(20+1)(20*2+1)/6= 2870

sum of consecutive squares up to 20^2

### 21(21+1)(2*21+1)/6= 3311

sum of consecutive squares up to 21^2

### n(a+z)/2

sum of numbers in an arithmetic series (n is number of terms, a is the lowest term, z is highest term)

### 2(r1)(r2)/(r1+r2)

average rate if d1=d2

### 17(4+100)/2= 884

sum of numbers in an arithmetic series from 4 to 100 with a constant difference of 6

### 20(5+100)/2= 1050

sum of numbers in an arithmetic series from 5 to 100 with a constant difference of 5

### 5(3+15)/2= 45

sum of numbers in an arithmetic series from 3 to 15 with a difference of 3

### 6(2+22)/2= 72

sum of numbers in an arithmetic series from 2 to 22 with a difference of 4

### 33(33+129)/2= 2673

sum of numbers in an arithmetic series from 33 to 129 with a constant difference of 3