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C2 - Arithmetic Progressions question.

New to this forum, so I'm sorry if I've posted in the wrong place!

I need help on a question:

In an AP, the 1st term is 13 and the 15th term is 111. Find the common difference and the sum of the first 20 terms.

I tried using the formula n/2(a+l), to work out the sum of the first 20 terms, but I got an answer of 1240. In the book, the answer is 1590.

Please help!!

Reply 1

AdrianDudek

Clearly the common difference is 7. The sum of the first n terms is:

S_n = n/2 (2a_1 +(n-1)d)

where a_1 is the first term, and d is the common difference.

S_20 = 20/2 (2x13 + (20-1)x7)

= 10 (26+133)

= 10 (159)

= 1590

Mwa.

Reply 2

gdunne42

Original post by PinkEye

U_n = a + (n-1)d

111 = 13 + 14d

solve for d

You can't use n/2(a+l) unless you work out the value of the 20th term

Reply 3

elldeegee

Original post by AdrianDudek

Clearly the common difference is 7. The sum of the first n terms is:
S_n = n/2 (2a_1 +(n-1)d)

where a_1 is the first term, and d is the common difference.
S_20 = 20/2 (2x13 + (20-1)x7)
= 10 (26+133)
= 10 (159)
= 1590
Mwa.

you can't just say "clearly the common difference is..." you have to show your working to gain the full amount of marks and some people obviously aren't as shrewd as you!

OP, use the menthod above AFTER using the method described below:

Original post by gdunne42