1.

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

Answer»

In the given AP, a = 6 d = (10 - 6) = 4

Suppose that there are n terms in the given AP.

Then, Tn = 174

\(\Rightarrow\) a + (n - 1) d = 174

\(\Rightarrow\) 6 + (n - 1) x 4 = 174

\(\Rightarrow\) 2 + 4n = 174

\(\Rightarrow\) 4n = 172

\(\Rightarrow\) n = 43

Hence, there are 43 terms in the given AP.

a=6

d=4

Tn=174

We know that, Tn= a+(n-1)d

                         174=6+(n-1)4

Solve for n to find the no. of terms.

Therefore, n= 43

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