Find the sum of the following APs: (i) 2, 7, 12, . . ., to 10 terms. (ii) –37, –33, –29, . . ., to 12 terms. (iii) 0.6, 1.7, 2.8, . . ., to 100 terms. (iv)

Question

Find the sum of the following APs: (i) 2, 7, 12, . . ., to 10 terms. (ii) &#x2013;37, &#x2013;33, &#x2013;29, . . ., to 12 terms. (iii) 0.6, 1.7, 2.8, . . ., to 100 terms. (iv)

Philoid · Accepted Answer

(i) Here, a = 2, d = 5 and n = 10

Sum of n terms can be given as follows:

S₁₀

= 5(4 + 45)

= 5

= 245

Thus, sum of the 10 terms of given AP (S_n)=245

(ii) Here, a = - 37, d = 4 and n = 12

Sum of n terms can be given as follows:

S₁₂

= 6(-74 + 44)

= 6

=-180

Thus, sum of the 12 terms of given AP (S_n)= -180

(iii) Here, a = 0.6, d = 1.1 and n = 100

Sum of n terms can be given as follows:

S₁₀₀

= 50(1.2 + 108.9)

= 50

=5505

Thus, sum of the 100 terms of given AP (S_n)= -5505

(iv) Here,

a= , n = 11,

d =

Sum of n terms can be given as follows:

S₁₁

= (+ )

=

Thus, sum of the 100 terms of given AP (S_n)=

Find the sum of the following APs:(i) 2, 7, 12, . . ., to 10 terms.(ii) –37, –33, –29, . . ., to 12 terms.(iii) 0.6, 1.7, 2.8, . . ., to 100 terms.(iv)

Find the sum of the following APs:
(i) 2, 7, 12, . . ., to 10 terms.

(ii) –37, –33, –29, . . ., to 12 terms.

(iii) 0.6, 1.7, 2.8, . . ., to 100 terms.

(iv)