How Many Terms Are There in the Ap 6,1 0, 14, 18, ….., 174? - Mathematics

How many terms are there in the AP 6,1 0, 14, 18, ….., 174?

In the given AP, a = 6 and d = (10-6) = 4
Suppose that there are n terms in the given AP.
Then, `T_n = 174 `

⇒ a+ (n-1) d =174

⇒ 6+ (n-1) × 4 = 174

⇒ 2+ 4n = 174

⇒ 4n = 172

⇒ n= 43
Hence, there are 43 terms in the given AP.

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अध्याय 11: Arithmetic Progression - Exercises 1

अध्याय 11 Arithmetic Progression
Exercises 1 | Q 7

The first term of an A.P. is 5 and its 100^th term is -292. Find the 50^th term of this A.P.

Find the 37^th term of the AP 6 , 7 `3/4 , 9 1/2 , 11 1/4,.............`

If S_n denotes the sum of the first n terms of an A.P., prove that S₃₀ = 3 (S₂₀ − S₁₀) ?

If m times the m^th term of an Arithmetic Progression is equal to n times its n^th term and m ≠ n, show that the (m + n)^th term of the A.P. is zero.

The 11^th term of the AP: `-5, (-5)/2, 0, 5/2, ...` is ______.

If the common difference of an AP is 5, then what is a₁₈ – a₁₃?

For the AP: –3, –7, –11, ..., can we find directly a₃₀ – a₂₀ without actually finding a₃₀ and a₂₀? Give reasons for your answer.

Write the first three terms of the APs when a and d are as given below:

a = `sqrt(2)`, d = `1/sqrt(2)`

Find the 20^th term of the AP whose 7^th term is 24 less than the 11^th term, first term being 12.

Justify whether it is true to say that the following are the n^th terms of an AP.

3n² + 5