Tag: sequences

My Arithmetic Sequence

My Arithmetic Sequence: -27, -24, -21, -18, -15

How to find t_{50}: First we use the following equation

t_{50} = t_1 + (n-1) (d)

then we substitute t_1 for the first term in the equation which is -27. We also substitute n with 50 and d with the pattern difference.

$latex t_{50} = -27+  (50-1) (3

then we solve for t_{50}

t_{50} = -27 + (49)(3)

t_{50} = -27 + 147

t_{50} = 120

The general equation for t_n is : 3n30

Now we solve for s_{50} by plugging in the numbers again

s_n = \frac{n}{2} (2 t_1 + (n-1)(d)

s_{50} = \frac{50}{2} ( 2(-27) + (50-1)(3)

s_{50} = 25( -54 + 147)

s_{50} = 25(93)

s_{50} = 2325