if (10-a)k , (a+2) are in AP , then find value of K
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Answers
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Answer:
Given
a
1
+a
5
+a
10
+a
15
+a
20
+a
24
=225
Let first term =a and
common difference=d
then General term T
n
=a+(n−1)d
Now,
a
1
+a
5
+a
10
+a
15
+a
20
+a
24
=225
⇒a+a+4d+a+9d+a+14d+a+19d+a+23d=225
⇒6a+69d=225
⇒2a+23d=75..
Step-by-step explanation:
Given
a
1
+a
5
+a
10
+a
15
+a
20
+a
24
=225
Let first term =a and
common difference=d
then General term T
n
=a+(n−1)d
Now,
a
1
+a
5
+a
10
+a
15
+a
20
+a
24
=225
⇒a+a+4d+a+9d+a+14d+a+19d+a+23d=225
⇒6a+69d=225
⇒2a+23d=75.....… (1)
sum of first 24 terms
=(
2
n
)[2a+(n−1)d]
=(
2
24
)[2a+(24−1)d]
=12(2a+23d)
=12×75.............[from (1)]
=900