Question

Sums of Ap 40,36,32,28,....to 15 terms​

Answer 1

Given :

Ap : 40, 36 , 32

To find :

Sum of 15 terms

Formula used :

$\sf \implies \: S_n \:=\: \: \bigg( \: \dfrac{n}{2} \: \bigg) \bigg( \: 2a \: + \: ( n- 1) d \: \bigg)$

Here,

• Sₙ = sum of n terms
• a = First term
• n = Number of terms
• d = common difference

SOLUTION :

First of all we need to find common difference,

d = Second term - First term

d = 36 - 40

d = -4

$\sf \implies \: S_{15} \:=\: \: \bigg( \: \dfrac{15}{2} \: \bigg) \bigg( \: 2 \times 40 \: + \: ( 15- 1) ( - 4)\: \bigg) \\ \\ \sf \implies \: S_{15} \:=\: \: \bigg( \: \dfrac{15}{2} \: \bigg)\bigg( \: 80\: + \: ( 14) ( - 4)\: \bigg) \\ \\ \sf \implies \: S_{15} \:=\: \: \bigg( \: \dfrac{15}{2} \: \bigg)\bigg( \: 80\: - 56\: \bigg) \\ \\ \sf \implies \: S_{15} \:=\: \: \bigg( \: \dfrac{15}{2} \: \bigg)\bigg( \:24\bigg) \\ \\ \sf \implies \: S_{15} \:=\: \dfrac{360}{2} \\ \\ \sf \implies \: S_{15} \:=\: \bold{180}$

ANSWER :

Sum of 15 terms = 180