Question

if the sum of the 16 term of an ap is 1624 and the first term is 500 times the common difference, then find the common difference​

Answer 1

S= n/2(2a(n-1)d

1624=16/2(2(500d)(16-1)d

1624=8*1000d*15d

1624/8=15000d

203=15000d

d = 15000/203

d= 73

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Answer 2

Answer:

Common difference is 0.2

Step-by-step explanation:

Let d be the common difference and a be the first term of the AP,

According to the question,

a = 500d,

Now, the sum of 16 terms of the sequence,

$S_{16}= \frac{16}{2}(2a + (16-1)d)$

$1624 =8(2(500d) + 15d)$

$1624 = 8(1000d + 15d)$

$203 = 1015d$

$\implies d =\frac{203}{1015}=\frac{1}{5}=0.2$

Hence, common difference is 0.2.

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