5+4(1) + 5+4(12) = 10+4(13)

5+4(2) + 5+4(11) = 10+4(13)

5+4(3) + 5+4(10) = 10+4(13)

You can see that these are all going to be the same and, since there are 12 terms,

2S = 12(10+4(13)) or 12*62

So S will be half of that or 6*62, which is 372.

Step-by-step explanation:

The sum you are looking for is 5+4(1) + 5+4(2)+…+ 5+4(11) + 5+4(12). Let’s call this sum S.

If you wrote the sum out starting from the last term and going backwards to the first term, it wouldn’t change the sum. It would still be S.

So let’s add these sums together to get another sum which will be 2S. We will add the first term to the last term and the second term to the second to last term, etc.

Answer: 10,400

let

a1 = 12

a30 = 244

d = ?

S50 = ?

an = a1 + (n - 1)d

a30 = a1 + (30 - 1)d

244 = 12 + 29d

244 - 12 = 29d

232 = 29d

8 = d

Sn = ½ n [ 2a1 + (n - 1)d ]

S50 = ½ (50) [ 2(12) + (50 - 1)8 ]

S50 = 25 [ 24 + (49)8 ]

S50 = 25 [ 24 + 392 ]

S50 = 25 [ 416 ]

S50 = 10,400