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Add : 7 + 10 {1}{2}+ 14 + ....... + 84

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Add : $7 + 10 \frac{1}{2} + 14 + ....... + 84$

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7 + 10 1/2 + 14.......84

The above series forms an Arithmetic progression (A.P) with first term

a = 7

& the common difference

d = 3.5

we know that the

n^{t h}

term of A.P is given by

a + (n - 1) d

here

a + (n - 1) d = 84

7 + (n - 1) 3.5 = 84

7 + (n - 1) 3.5 = 84

7 + (n - 1) 3.5 - 7 = 84 - 7

[ subtract

7

from sides]

(n - 1) 3.5 = 77

divide both sides by

3.5

(n - 1) = 77/3.5

(n - 1) = \frac{77 \times 10}{35}

(n - 1) = 22

Add

1

on both sides

n = 23

\Rightarrow 84

is the

2 3^{r d}

term

Sum of

n

terms of A.P is given by

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

n = 23, a = 7, d = 3.5

\Rightarrow S_{n} = \frac{23}{2} [2 (7) + (23 - 1) 3.5]

S_{n} = \frac{23}{2} [14 + 22 (3.5)]

S_{n} = \frac{23}{2} [14 + 77]

S_{n} = \frac{23}{2} [91]

S_{n} = \frac{23}{2} \times 91

S_{n} = 1046.5

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Question Text	Add : $7 + 10 \frac{1}{2} + 14 + ....... + 84$
Answer Type	Text solution:1
Upvotes	150

Add : 7+1021​+14+.......+84

Text solutionVerified

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Add : $7 + 10 \frac{1}{2} + 14 + ....... + 84$