We read your photo as:

Each term of A.P is doubled. Is the resulting sequence also an A.P ? If it is write its first term.

Mathematics

ScanSolve AI Answer

Answer

0

Step-by-step solution

5 steps
  1. Write the expressions for the 7th7^{th} and 11th11^{th} terms of an A.P.

    Let the first term be aa and the common difference be dd. The nthn^{th} term of an A.P. is given by an=a+(n−1)da_n = a + (n-1)d.
    The 7th7^{th} term is a7=a+(7−1)d=a+6da_7 = a + (7-1)d = a + 6d.
    The 11th11^{th} term is a11=a+(11−1)d=a+10da_{11} = a + (11-1)d = a + 10d.

  2. Set up the equation based on the given condition.

    The problem states that 7 times the 7th7^{th} term is equal to 11 times the 11th11^{th} term:

    7×a7=11×a117 \times a_7 = 11 \times a_{11}

    Substitute the expressions from Step 1:

    7(a+6d)=11(a+10d)7(a + 6d) = 11(a + 10d)
  3. Solve the equation for aa in terms of dd.

    7a+42d=11a+110d7a + 42d = 11a + 110d

    Subtract 7a7a from both sides:

    42d=4a+110d42d = 4a + 110d

    Subtract 110d110d from both sides:

    42d−110d=4a42d - 110d = 4a −68d=4a-68d = 4a

    Divide by 4:

    a=−68d4a = \frac{-68d}{4} a=−17da = -17d
  4. Find the expression for the 18th18^{th} term.

    The 18th18^{th} term is a18=a+(18−1)d=a+17da_{18} = a + (18-1)d = a + 17d.

  5. Substitute the value of aa from Step 3 into the expression for the 18th18^{th} term.

    a18=(−17d)+17da_{18} = (-17d) + 17d a18=0a_{18} = 0

    Thus, the 18th18^{th} term of the A.P. is 0\boxed{0}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp