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Question

If a5=12 and a15=400. Find S10

A
314
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B
320
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C
316
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D
318
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Solution

The correct option is A 314
Using the formula,
an=a+(n1)d
So, a5=a+(51)d
12=a+4d ............. (1)
a15=a+(151)d
400=a+14d .......... (2)
Solving equation (1) & (2)
12=a+4d
400=a+14d
(-) (-) (-)
---------------------
388=10d
d=38.8
Put the value of d in equation (1)
12=a+4(38.8)
12=a+155.2
a=143.2
The sum of first n term is given by Sn=n2(2a+(n1)d)
S10=102(2(143.2)+(101)38.8)
=5(286.4+349.2)
=5(62.8)
S10=314

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