Question

The sum of first 15 terms of an ap is 112 and the sum of its next four terms is 518 find the ap​

Answer 1

Answer:

PLZ MARK AS BRAINLIEST

Answer 2

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Correct Question :- \: \star}}}}}$

The sum of first 16 terms of an AP is 112 and the sum of its next fourteen terms is 518. Find the AP.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

First term is - 8 and common difference is 2.

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

→ Sn = n/2 × [2a + (n - 1)d]

→ S16 = 16/2 × [2a + (16 - 1)d]

→ 112 = 8 × (2a + 15d)

→ 14 = 2a + 15d __(1)

Now S16 + S14 = S30

→ 112 + 518 = 630

→ S30 = 30/2 × [2a + (30 - 1)d]

→ 630 = 15 × (2a + 29d)

→ 42 = 2a + 29d __(2)

On doing eq(2) - eq(1)

→ 28 = 14d

→ d = 2

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

14 = 2a + 30

→ a = - 8

$\mathfrak{\huge{\pink{\underline{\underline{So,}}}}}$

First term is - 8 and common difference is 2.