Question:
$(5+13+21+\ldots+181)=?$
(a) 2476
(b) 2337
(c) 2219
(d) 2139
Solution:
(d) 2139
Here, a = 5, d = (13-5) = 8 and l = 181
Let the number of terms be n.
Then Tn = 181
⇒a + (n-1) d = 181
⇒ 5 + ( n -1) ⨯ 8 = 181
⇒ 8n = 184
⇒ n = 23
$\therefore$ Required sum $=\frac{n}{2}(a+l)$
$=\frac{23}{2}(5+181)=23 \times 93=2139$
Hence, the required sum is 2139.
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