Question

Q- Find the sum of first 22 terms of an ap if it's common diffrence is 6 and third and fourth terms are 19 and 25 respectively.
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Answer 1

Answer:

1463

Step-by-step explanation:

S₂₂ = ?

d = 6

a₃ = 19 = a + 2d ⇒ a + 12 = 19 ⇒ a = 7

a₄ = 25 = a + 3d ⇒ a + 18 = 25 ⇒ a = 7

S₂₂ = 22[7 + 21(6)]/2 ⇒ 11 (7 + 126) ⇒ 11 x 133 = 1463

Hope this helps.....

Answer 2

Answer:

• Sum of first 22 terms = 1540.

Step-by-step explanation:

Given:

• Common difference (d) = 6
• Third term (a₃) = 19
• Fourth term (a₄) = 25

To Find:

• Sum of first 22 term.

Formula used:

• aₙ = a + (n - 1)d   .......(1)
• Sₙ = n/2[2a + (n - 1)d]    .....(2)

Now, it is given that 3rd term is 19.

⇒ a₃ = a + 2d

⇒ 19 = a + 2(6)

⇒ 19 = a + 12

⇒ a = 7

Now, put the value of 'a' in Equation (2).

⇒ Sₙ = n/2[2a + (n - 1)d]

⇒ S₂₂ = 22/2[2 × 7 + (22 - 1)6]

⇒ S₂₂ = 11[14 + (21)6]

⇒ S₂₂ = 11[14 + 126]

⇒ S₂₂ = 11[140]

⇒ S₂₂ = 1540

Hence, Sum of first 22 terms = 1540.