Find the sum of the following (i) 3, 7, 11,… up to 40 terms.(ii) 10

1.	Find the sum of the following (i) 3, 7, 11,… up to 40 terms.(ii) 102, 97, 92,… up to 27 terms.(iii) 6 + 13 + 20 + …. + 97
Answer» (i) 3,7,11,… up to 40 terms First term (a) = 3 Common difference (d) = 7 – 3 = 4 Number of terms (n) = 40 S_n = (n/2) [2a + (n – 1) d] S₄₀ = (40/2) [6 + 39 x 4] = 20 [6 + 156] = 20 x 162 S₄₀ = 3240 (ii) Here a = 102, d = 97 – 102 = -5 n = 27 S_n = (n/2) [2a + (n – 1)d] S₂₇ = (27/2) [2(102) + 26(-5)] = (27/2) [204 – 130] = (27/2) x 74 = 27 x 37 = 999 S₂₇ = 999 (iii) Here a = 6, d = 13 – 6 = 7, l = 97 n = (l - a)/d + 1 = (97 - 6)/7 + 1 = 91/7 + 1 = 13 + 1 = 14 S_n = (n/2) (a + l) S_n = (14/2) (a + l) S_n = (14/2) (6 + 97) = 7 x 103 S_n = 721

Find the sum of the following (i) 3, 7, 11,… up to 40 terms.(ii) 102, 97, 92,… up to 27 terms.(iii) 6 + 13 + 20 + …. + 97

Answer»

(i) 3,7,11,… up to 40 terms

First term (a) = 3

Common difference (d) = 7 – 3 = 4

Number of terms (n) = 40

S_n = (n/2) [2a + (n – 1) d]

S₄₀ = (40/2) [6 + 39 x 4] = 20 [6 + 156]

= 20 x 162

S₄₀ = 3240

(ii) Here a = 102, d = 97 – 102 = -5

n = 27

S_n = (n/2) [2a + (n – 1)d]

S₂₇ = (27/2) [2(102) + 26(-5)]

= (27/2) [204 – 130]

= (27/2) x 74

= 27 x 37 = 999

S₂₇ = 999

(iii) Here a = 6, d = 13 – 6 = 7, l = 97

n = (l - a)/d + 1

= (97 - 6)/7 + 1

= 91/7 + 1

= 13 + 1 = 14

S_n = (n/2) (a + l)

S_n = (14/2) (a + l)

S_n = (14/2) (6 + 97)

= 7 x 103

S_n = 721