If the last term of an A.P. of 30 terms is 119 and the $8^{th}$ term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of th

Question

If the last term of an A.P. of 30 terms is 119 and the $8^{th}$ term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.

Accepted Answer

Step 1: Last term $a_n = 119 \Rightarrow a + 29d = 119$ ... (i)
Step 2: $8^{th}$ term from end $= 23^{rd}$ term from the beginning
$\Rightarrow a + 22d = 91$ ... (ii)
Step 3: Solving (i) and (ii), we get
$a = 3$ and $d = 4$
Step 4: $	herefore S_{30} = \frac{n}{2}(a + l)$
$= \frac{30}{2}(3 + 119)$
$= 1830$

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