Question

If 8th term of an AP is 15, the Sum of the 15 its term is​

Answer 1

Answer:

Sum of the 15 its term is 225.

Step-by-step explanation:

Given

• 8th term of an AP is 15 

To find :

• sum of first 15  terms of AP =? 

solution :

we know that 

$\bf \: S_n = \frac{n}{2} \{2a + (n - 1)d \} \: \: \: \: \: \: and \\ \\ \bf \: a_n = a + (n - 1)d \\ \\ \red{ \bf \: here} \\ \bf a_8 = 15 \\ \sf \: so \\ \bf \: { \: a + (n - 1)d = 15 \: \: \: \: \: }\\ \bf \implies\: a + (8 - 1)d = 15 \\ \bf \implies\: \pink{ a + 7d = 15 \: \: \: - - - (1)} \: \\ \bf \: now \\ \\ \bf \: S_{15} = \frac{15}{2} \{2a + (15 - 1)d \} \\ \bf \implies\: S_n = \frac{15}{2} (2a + 14d) \\ \bf \implies\: S_n = \frac{15}{2} \times 2 \pink{(a + 7d)} \\ \bf \implies\: S _n = 15 \times \pink{15 }\\ \bf \implies\: S_n = 225$

$\bf\:\therefore\:S_{15} \:=\:225$

Answer 2

Answer:

225 Same as above

8a = a₁ + 7d

Hence

a₁ + 7d = 15 ...(i)

S15 n 2 = [2a₁ + (15-1)d]

S15 = 1/5 [201 2 [2a₁ + 14d]

= 15(a₁ + 7d)

= 15(15) ...from i = 225.