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Find the sum of the following APS.
Arithmetic Progression | CBSE | Class 10 | Maths | NCERT
Find the sum of the following APS.

(i) 2,7,12, \ldots ., to 10 terms.

(ii) -37,-33,-29, \ldots, to 12 terms

Solutions:

(i) Provided that, 2,7,12, \ldots, to 10 terms

And for this A.P.,

The first term, \mathrm{a}=2

And the common difference, d=a_{2}-a_{1}=7-2=5

n=10

We all know that,for sum of the nth term in the AP series the formula is,

S_{n}=n / 2[2 a+(n-1) d]

S_{10}=10 / 2[2(2)+(10-1) \times 5]

=5[4+(9) \times(5)]

=5 \times 49=245

(ii) Provided that, -37,-33,-29, \ldots, to 12 terms

And for this A.P.,

first term, \mathrm{a}=-37

And the common difference, d=a_{2}-a_{1}

d=(-33)-(-37)

=-33+37=4

n=12

We all know that, for sum of the nth term in the AP series the formula is,

\mathrm{S}_{\mathrm{n}}=\mathrm{n} / 2[2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d}]

\mathrm{S}_{12}=12 / 2[2(-37)+(12-1) \times 4]

=6[-74+11 \times 4]

=6[-74+44]

=6(-30)=-180

i

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