LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

ARITHMETIC PROGRESION - FINDING TERMS FROM END OF AP

**To Find the eth Term From The End Of An A.P. –
**

__Theorem.2) -__ Let ‘a’ be the 1st term, ‘d’ be the common difference and ‘l’ be the last term of a given A.P. Then, prove that its eth term from the end is {l – (e – 1) d}.

__Proof -__ We may write the given A.P. as

**a, (a + d), (a + 2d), (a + 3d),……………(l – 2d), (l – d), l.
**

**then we have
**

**last term = l = [l – (1 – 1) d
**

**2nd term from the end = l – d = [l – (2 – 1) d]
**

**3rd term from the end = l – 2d = [l – (3 – 1) d]
**

**…………… ……………. …………………
**

**…………… ………………. …………………
**

**So, eth term from the end = l – (e – 1) d
**

**Example.) Find the 10th term from the end of the A.P. 4, 9, 14, ………….., 254
**

**Ans.) The given A.P. is 4, 9, 14,………………….
**

**Where, a = 4, d = (9 – 4) = (14 – 9) = 5 (constant), l = 254, and e = 10.
**

**Now, 10th term from the end = {l – (e – 1) d}
**

** = [254 – {(10 – 1) X 5}]
**

** = {254 – (9 X 5)}
**

** = (254 – 45) = 209
**

**Hence, the 10th term from the end is 209. (Ans.)**

Your second block of text...