Question

The sum of first six terms of an AP is 36 and that of first 16 terms is 256. Find the sum of first

10 terms.
​

Answer 1

Step-by-step explanation:

10th

Maths

Arithmetic Progressions

Sum of an AP

If sum of first 6 terms of ...

MATHS

If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.

MEDIUM

ANSWER

We have the sum of first n terms of an AP,

S

n

=

2

n

[2a+(n−1)d]

Given,

36=

2

6

[2a+(6−1)d]

12=2a+5d ---------(1)

256=

2

16

[2a+(16−1)d]

32=2a+15d ---------(2)

Subtracting, (1) from (2)

32−12=2a+15d−(2a+5d)

20=10d ⟹d=2

Substituting for d in (1),

12=2a+5(2)=2(a+5)

6=a+5 ⟹a=1

∴ The sum of first 10 terms of an AP,

S

10

=

2

10

[2(1)+(10−1)2]

S

10

=5[2+18]

S

10

=100

This is the sum of the first 10 terms

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